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

1,1

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A085317, A004434, A193141, A193143.

Sequence in context: A087537 A117840 A296012 * A033250 A139922 A112795

Adjacent sequences: A193139 A193140 A193141 * A193143 A193144 A193145

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 16 2011

Status

approved