A269960 Integers n such that the n-th golden rectangle number is the sum of 4 but no fewer nonzero squares.

4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 83, 84, 88, 94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 179, 180, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 275, 276, 280, 286, 292, 298, 304, 310, 316, 322, 328, 334, 335

Offset

1,1

Comments

Golden rectangle numbers equal the partial sums of squares of Fibonacci numbers.

Corresponding golden rectangle numbers are 15, 4895, 1576239, 507544127, 163427632719, 52623190191455, ...

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

4 is a term because 1^2 + 1^2 + 2^2 + 3^2 = 3*5 = x^2 + y^2 + z^2 has no solution for integer x, y and z.
5 is not a term because 1^2 + 1^2 + 2^2 + 3^2 + 5^2 = 5*8 = 2^2 + 6^2.

Prog

(PARI) isA004215(n)= my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri-7 ; if( j % 8==0, return(1) ) ; ); fouri *= 4 ; ) ; return(0) ;
a001654(n) = fibonacci(n)*fibonacci(n+1);
for(n=1, 1e3, if(isA004215(a001654(n)), print1(n, ", ")));

Crossrefs

Cf. A001654, A004215, A016957.

Sequence in context: A310532 A189932 A310533 * A016957 A109273 A294636

Adjacent sequences: A269957 A269958 A269959 * A269961 A269962 A269963

Keyword

nonn

Author

Altug Alkan, Mar 08 2016

Status

approved