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A193142 Primes which are the sum of 5 distinct positive squares. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 13:36 EDT 2020. Contains 337264 sequences. (Running on oeis4.)