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

Author

Reinhard Zumkeller, Nov 19 2002

Keywords

• nonn
• easy

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]

Examples

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

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

Crossrefs

Cf. A078134, A078139, A078132.

Programs

Mathematica

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

PARI

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

Extensions

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