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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 20 02:01 EDT 2019. Contains 328244 sequences. (Running on oeis4.)