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%I #9 Mar 11 2016 23:04:53
%S 6,8,17,34,35,60,61,62,67,72,73,74,88,114,116,126,128,144,145,146,165,
%T 171,210,212,223,231,237,247,257,269,283,288,289,290,303,317,324,325,
%U 326,330,332,339,346,347,354,356,360,361,362,376,402,404,415,423,429,438,440
%N Integers n such that product of first n nonzero Fibonacci numbers (A003266) is the sum of 4 but no fewer nonzero squares.
%C How is the distribution of a(n), a(n+1), a(n+2) in this sequence where a(n+2) = a(n+1) + 1 = a(n) + 2?
%H Chai Wah Wu, <a href="/A270046/b270046.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 is a term because 1*1*2*3*5*8 = 240 and 240 = x^2 + y^2 + z^2 has no solution for integer values of x, y and z.
%o (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);
%o a003266(n) = prod(k=1, n, fibonacci(k));
%o for(n=1, 1e3, if(isA004215(a003266(n)), print1(n, ", ")));
%Y Cf. A003266, A004215.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 09 2016
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