A193142 Primes which are the sum of 5 distinct positive squares.

79, 103, 127, 131, 139, 151, 157, 163, 167, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 16 2011

Keywords

• nonn

Comments

A004434 INTERSECTION A000040. [Charles R Greathouse IV, Jul 17 2011]

Examples

			79=1^2+2^2+3^2+4^2+7^2, 103=2^2+3^2+4^2+5^2+7^2, 127=1^2+2^2+3^2+7^2+8^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A085317, A004434, A193141, A193143.

Programs

Mathematica

lst = {}; Do[Do[Do[Do[Do[p = a^2 + b^2 + c^2 + d^2 + e^2; If[PrimeQ[p], AppendTo[lst, p]], {e, d - 1, 1, -1}], {d, c - 1, 1, -1}], {c, b - 1, 1, -1}], {b, a - 1, 1, -1}], {a, 6, 20}]; OEISTrim[Take[Union[lst], 80]]
With[{upto=500},Select[Union[Total/@Subsets[Range[Ceiling[Sqrt[upto-30]]]^2, {5}]],PrimeQ[#]&&#<=upto&]] (* Harvey P. Dale, Jun 05 2016 *)

PARI

upto(lim)=my(v=List(),tb,tc,td,te);for(a=6,sqrt(lim),for(b=4,min(a-1,sqrt(lim-a^2)),tb=a^2+b^2;for(c=3,min(b-1,sqrt(lim-tb)),tc=tb+c^2;for(d=2,min(c-1,sqrt(lim-tc)),td=tc+d^2;forstep(e=1+td%2,d-1,2,te=td+e^2;if(te>lim,break);if(isprime(te),listput(v,te)))))));vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Jul 17 2011

Formula

Conjecture: a(n) = prime(n+32) for n > 13. [Charles R Greathouse IV, Jul 17 2011]