A078138 Primes which can be written as sum of squares > 1.

13, 17, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset

1,1

Comments

By Sylvester's solution to the Frobenius problem, all integers greater than 4*9 - 4 - 9 = 23 can be represented as a sum of multiples of 4 and 9. Hence all primes except 2,3,5,7,11,19,23 are in this sequence. [Charles R Greathouse IV, Apr 19 2010]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

J. J. Sylvester, "Question 7382" in Mathematical Questions from the Educational Times, 37 (1884), p. 26 (search for 7382).

Eric Weisstein's World of Mathematics, Sum of Squares Function

Eric Weisstein's World of Mathematics, Coin Problem

Index entries for sequences related to sums of squares

Example

A000040(11) = 31 = 3^2 + 3^2 + 3^2 + 2^2, therefore 31 is a term.

Mathematica

Join[{13, 17}, Prime[Range[10, 100]]] (* Harvey P. Dale, May 12 2014 *)

Prog

(PARI) a(n)=if(n<3, [13, 17][n], prime(n+7))

Crossrefs

Cf. A078134, A078139, A078132.

Sequence in context: A283294 A283217 A283390 * A164074 A152426 A152427

Adjacent sequences: A078135 A078136 A078137 * A078139 A078140 A078141

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 19 2002

Extensions

Comments, reference, and links by Charles R Greathouse IV, Apr 19 2010

Status

approved