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A269931
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Integers n such that the sum of squares of the first n primes (A024450) is the sum of 4 but no fewer nonzero squares.
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1
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4, 12, 20, 28, 29, 36, 44, 49, 52, 57, 60, 68, 73, 76, 84, 92, 100, 105, 108, 116, 124, 132, 140, 148, 153, 156, 161, 164, 172, 180, 188, 189, 196, 201, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 281, 284, 289, 292, 300, 308, 316, 324, 329, 332, 340, 345, 348, 356, 364, 372
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OFFSET
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1,1
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COMMENTS
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Terms that are not divisible by 4 are 29, 49, 57, 73, 105, 153, 161, 189, 201, 281, 289, 329, 345, 373, 385, 409, 417, 449, 457, 529, 553, 617, 633, 641, 645, ...
Corresponding values of sum of squares of the first n primes are 87, 4727, 30007, 98055, 109936, 239087, 486655, 710844, 874695, 1203356, 1432487, 2210983, 2841372, 3270831, ...
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LINKS
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EXAMPLE
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4 is a term because 2^2 + 3^2 + 5^2 + 7^2 = 87 and 87 = x^2 + y^2 + z^2 has no solution for integer x, y and z.
5 is not a term because 2^2 + 3^2 + 5^2 + 7^2 + 11^2 = 208 = 8^2 + 12^2.
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MATHEMATICA
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Select[Range@ 372, Nand[SquaresR[4, #] > 1, Or[SquaresR[3, #] > 1, SquaresR[2, #] > 1, IntegerQ@ Sqrt@ #]] &@ Total[Prime[Range@ #]^2] &] (* Michael De Vlieger, Mar 08 2016 *)
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PROG
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(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) ;
a024450(n) = sum(k=1, n, prime(k)^2);
for(n=1, 1e3, if(isA004215(a024450(n)), print1(n, ", ")));
(PARI) list(lim)=my(v=List(), n, s); forprime(p=2, , s+=p^2; if(n++>lim, return(Vec(v))); if(s\4^valuation(s, 4)%8==7, listput(v, n))) \\ Charles R Greathouse IV, Mar 08 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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