A269931 Integers n such that the sum of squares of the first n primes (A024450) is the sum of 4 but no fewer nonzero squares.

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

Offset

1,1

Comments

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, ...

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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 *)

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) ;
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

Crossrefs

Cf. A004215, A024450.

Sequence in context: A227226 A242118 A030387 * A043437 A213258 A369037

Adjacent sequences: A269928 A269929 A269930 * A269932 A269933 A269934

Keyword

nonn

Author

Altug Alkan, Mar 08 2016

Status

approved