A118591 Larger of two consecutive primes whose sum is a square.

19, 53, 73, 293, 883, 1153, 1931, 2593, 3529, 4051, 6053, 7207, 7451, 15139, 20809, 21647, 24203, 26921, 28807, 34849, 46819, 53147, 56453, 69193, 74507, 83233, 84053, 98573, 103067, 103969, 109517, 110459, 112339, 136247, 149059, 151253

Offset: 1

Author

Cino Hilliard, May 08 2006

Keywords

• easy
• nonn

Examples

			17 and 19 are consecutive primes whose sum is 36, a square, so 19 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..600 from Harvey P. Dale)

Crossrefs

Cf. A061275, A151800.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[14000]],2,1],IntegerQ[ Sqrt[ Total[#]]]&]] [[2]] (* Harvey P. Dale, May 03 2012 *)

PARI

g(n) = for(x=2,n,if(issquare(prime(x)+prime(x-1)),print1(prime(x)",")))

PARI

lista(pmax) = {my(p1 = 2); forprime(p2 = 3, pmax, if(issquare(p1 + p2), print1(p2, ", ")); p1 = p2);} \\ Amiram Eldar, Jul 12 2024

Formula

a(n) = A151800(A061275(n)). - Amiram Eldar, Jul 12 2024