fibos1

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Script Name fibos1
Description The sum of the squares of two consecutive Fibonacci numbers is a Fibonacci number https://twitter.com/AlgebraFact/status/780423101272186884
Area SQL General
Contributor Sokrates https://twitter.com/MatthiasRogel
Created Monday September 26, 2016

Statement 1

with fibos as 
( 
  select  
     level as n, 
     (power((1+sqrt(5))/2, level) - power((1-sqrt(5))/2, level)) / (sqrt(5)) as fibo 
  from 
     dual 
  connect by 
     level <= 100 
) 
select 
   f1.n, round(f1.fibo) as "f(n)", round(f2.fibo) as "f(n+1)", round(f3.fibo) as "f(2n+1)", 
   'f(' || f1.n || ') ^ 2 + f(' || f2.n || ') ^ 2 = f(' || round(f3.n) || ')' as is_true 
from 
   fibos f1, fibos f2, fibos f3 
where 
   f2.n = f1.n + 1 and 
   f3.n = 2* f1.n + 1 and 
   abs(f1.fibo * f1.fibo + f2.fibo * f2.fibo - f3.fibo) < 1e-10


N f(n) f(n+1) f(2n+1) IS_TRUE
1 1 1 2 f(1) ^ 2 + f(2) ^ 2 = f(3)
2 1 2 5 f(2) ^ 2 + f(3) ^ 2 = f(5)
3 2 3 13 f(3) ^ 2 + f(4) ^ 2 = f(7)
4 3 5 34 f(4) ^ 2 + f(5) ^ 2 = f(9)
5 5 8 89 f(5) ^ 2 + f(6) ^ 2 = f(11)
6 8 13 233 f(6) ^ 2 + f(7) ^ 2 = f(13)
7 13 21 610 f(7) ^ 2 + f(8) ^ 2 = f(15)
8 21 34 1597 f(8) ^ 2 + f(9) ^ 2 = f(17)
9 34 55 4181 f(9) ^ 2 + f(10) ^ 2 = f(19)
10 55 89 10946 f(10) ^ 2 + f(11) ^ 2 = f(21)
11 89 144 28657 f(11) ^ 2 + f(12) ^ 2 = f(23)
12 144 233 75025 f(12) ^ 2 + f(13) ^ 2 = f(25)
13 233 377 196418 f(13) ^ 2 + f(14) ^ 2 = f(27)
14 377 610 514229 f(14) ^ 2 + f(15) ^ 2 = f(29)
15 610 987 1346269 f(15) ^ 2 + f(16) ^ 2 = f(31)
16 987 1597 3524578 f(16) ^ 2 + f(17) ^ 2 = f(33)
17 1597 2584 9227465 f(17) ^ 2 + f(18) ^ 2 = f(35)
18 2584 4181 24157817 f(18) ^ 2 + f(19) ^ 2 = f(37)
19 4181 6765 63245986 f(19) ^ 2 + f(20) ^ 2 = f(39)
20 6765 10946 165580141 f(20) ^ 2 + f(21) ^ 2 = f(41)
21 10946 17711 433494437 f(21) ^ 2 + f(22) ^ 2 = f(43)
22 17711 28657 1134903170 f(22) ^ 2 + f(23) ^ 2 = f(45)
23 28657 46368 2971215073 f(23) ^ 2 + f(24) ^ 2 = f(47)
24 46368 75025 7778742049 f(24) ^ 2 + f(25) ^ 2 = f(49)
25 75025 121393 20365011074 f(25) ^ 2 + f(26) ^ 2 = f(51)
26 121393 196418 53316291173 f(26) ^ 2 + f(27) ^ 2 = f(53)
27 196418 317811 139583862445 f(27) ^ 2 + f(28) ^ 2 = f(55)
28 317811 514229 365435296162 f(28) ^ 2 + f(29) ^ 2 = f(57)
29 514229 832040 956722026041 f(29) ^ 2 + f(30) ^ 2 = f(59)
30 832040 1346269 2504730781961 f(30) ^ 2 + f(31) ^ 2 = f(61)
31 1346269 2178309 6557470319842 f(31) ^ 2 + f(32) ^ 2 = f(63)
32 2178309 3524578 17167680177565 f(32) ^ 2 + f(33) ^ 2 = f(65)
33 3524578 5702887 44945570212853 f(33) ^ 2 + f(34) ^ 2 = f(67)
34 5702887 9227465 117669030460994 f(34) ^ 2 + f(35) ^ 2 = f(69)
35 9227465 14930352 308061521170129 f(35) ^ 2 + f(36) ^ 2 = f(71)
36 14930352 24157817 806515533049393 f(36) ^ 2 + f(37) ^ 2 = f(73)
37 24157817 39088169 2111485077978050 f(37) ^ 2 + f(38) ^ 2 = f(75)
38 39088169 63245986 5527939700884757 f(38) ^ 2 + f(39) ^ 2 = f(77)
39 63245986 102334155 14472334024676221 f(39) ^ 2 + f(40) ^ 2 = f(79)
40 102334155 165580141 37889062373143906 f(40) ^ 2 + f(41) ^ 2 = f(81)
41 165580141 267914296 99194853094755497 f(41) ^ 2 + f(42) ^ 2 = f(83)
42 267914296 433494437 259695496911122585 f(42) ^ 2 + f(43) ^ 2 = f(85)
43 433494437 701408733 679891637638612258 f(43) ^ 2 + f(44) ^ 2 = f(87)
44 701408733 1134903170 1779979416004714189 f(44) ^ 2 + f(45) ^ 2 = f(89)
45 1134903170 1836311903 4660046610375530309 f(45) ^ 2 + f(46) ^ 2 = f(91)
46 1836311903 2971215073 12200160415121876738 f(46) ^ 2 + f(47) ^ 2 = f(93)
47 2971215073 4807526976 31940434634990099905 f(47) ^ 2 + f(48) ^ 2 = f(95)
48 4807526976 7778742049 83621143489848422977 f(48) ^ 2 + f(49) ^ 2 = f(97)
49 7778742049 12586269025 218922995834555169026 f(49) ^ 2 + f(50) ^ 2 = f(99)

49 rows selected.

N	f(n)	f(n+1)	f(2n+1)	IS_TRUE
1	1	1	2	f(1) ^ 2 + f(2) ^ 2 = f(3)
2	1	2	5	f(2) ^ 2 + f(3) ^ 2 = f(5)
3	2	3	13	f(3) ^ 2 + f(4) ^ 2 = f(7)
4	3	5	34	f(4) ^ 2 + f(5) ^ 2 = f(9)
5	5	8	89	f(5) ^ 2 + f(6) ^ 2 = f(11)
6	8	13	233	f(6) ^ 2 + f(7) ^ 2 = f(13)
7	13	21	610	f(7) ^ 2 + f(8) ^ 2 = f(15)
8	21	34	1597	f(8) ^ 2 + f(9) ^ 2 = f(17)
9	34	55	4181	f(9) ^ 2 + f(10) ^ 2 = f(19)
10	55	89	10946	f(10) ^ 2 + f(11) ^ 2 = f(21)
11	89	144	28657	f(11) ^ 2 + f(12) ^ 2 = f(23)
12	144	233	75025	f(12) ^ 2 + f(13) ^ 2 = f(25)
13	233	377	196418	f(13) ^ 2 + f(14) ^ 2 = f(27)
14	377	610	514229	f(14) ^ 2 + f(15) ^ 2 = f(29)
15	610	987	1346269	f(15) ^ 2 + f(16) ^ 2 = f(31)
16	987	1597	3524578	f(16) ^ 2 + f(17) ^ 2 = f(33)
17	1597	2584	9227465	f(17) ^ 2 + f(18) ^ 2 = f(35)
18	2584	4181	24157817	f(18) ^ 2 + f(19) ^ 2 = f(37)
19	4181	6765	63245986	f(19) ^ 2 + f(20) ^ 2 = f(39)
20	6765	10946	165580141	f(20) ^ 2 + f(21) ^ 2 = f(41)
21	10946	17711	433494437	f(21) ^ 2 + f(22) ^ 2 = f(43)
22	17711	28657	1134903170	f(22) ^ 2 + f(23) ^ 2 = f(45)
23	28657	46368	2971215073	f(23) ^ 2 + f(24) ^ 2 = f(47)
24	46368	75025	7778742049	f(24) ^ 2 + f(25) ^ 2 = f(49)
25	75025	121393	20365011074	f(25) ^ 2 + f(26) ^ 2 = f(51)
26	121393	196418	53316291173	f(26) ^ 2 + f(27) ^ 2 = f(53)
27	196418	317811	139583862445	f(27) ^ 2 + f(28) ^ 2 = f(55)
28	317811	514229	365435296162	f(28) ^ 2 + f(29) ^ 2 = f(57)
29	514229	832040	956722026041	f(29) ^ 2 + f(30) ^ 2 = f(59)
30	832040	1346269	2504730781961	f(30) ^ 2 + f(31) ^ 2 = f(61)
31	1346269	2178309	6557470319842	f(31) ^ 2 + f(32) ^ 2 = f(63)
32	2178309	3524578	17167680177565	f(32) ^ 2 + f(33) ^ 2 = f(65)
33	3524578	5702887	44945570212853	f(33) ^ 2 + f(34) ^ 2 = f(67)
34	5702887	9227465	117669030460994	f(34) ^ 2 + f(35) ^ 2 = f(69)
35	9227465	14930352	308061521170129	f(35) ^ 2 + f(36) ^ 2 = f(71)
36	14930352	24157817	806515533049393	f(36) ^ 2 + f(37) ^ 2 = f(73)
37	24157817	39088169	2111485077978050	f(37) ^ 2 + f(38) ^ 2 = f(75)
38	39088169	63245986	5527939700884757	f(38) ^ 2 + f(39) ^ 2 = f(77)
39	63245986	102334155	14472334024676221	f(39) ^ 2 + f(40) ^ 2 = f(79)
40	102334155	165580141	37889062373143906	f(40) ^ 2 + f(41) ^ 2 = f(81)
41	165580141	267914296	99194853094755497	f(41) ^ 2 + f(42) ^ 2 = f(83)
42	267914296	433494437	259695496911122585	f(42) ^ 2 + f(43) ^ 2 = f(85)
43	433494437	701408733	679891637638612258	f(43) ^ 2 + f(44) ^ 2 = f(87)
44	701408733	1134903170	1779979416004714189	f(44) ^ 2 + f(45) ^ 2 = f(89)
45	1134903170	1836311903	4660046610375530309	f(45) ^ 2 + f(46) ^ 2 = f(91)
46	1836311903	2971215073	12200160415121876738	f(46) ^ 2 + f(47) ^ 2 = f(93)
47	2971215073	4807526976	31940434634990099905	f(47) ^ 2 + f(48) ^ 2 = f(95)
48	4807526976	7778742049	83621143489848422977	f(48) ^ 2 + f(49) ^ 2 = f(97)
49	7778742049	12586269025	218922995834555169026	f(49) ^ 2 + f(50) ^ 2 = f(99)

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