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A269960
Integers n such that the n-th golden rectangle number is the sum of 4 but no fewer nonzero squares.
1
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, ...
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 08 2016
STATUS
approved