A206279 Smallest of three consecutive primes whose sum is a square.

13, 37, 277, 313, 613, 7591, 8209, 12157, 14557, 15679, 16267, 23053, 32233, 42953, 44887, 55213, 81013, 94687, 105649, 106397, 135241, 203317, 221401, 225769, 235747, 245941, 258707, 287671, 306541, 331333, 342049, 346111, 347443, 393853, 479191, 488827

Offset: 1

Author

Harvey P. Dale, Feb 05 2012

Keywords

• nonn

Examples

			a(4) = 313. The next two primes are 317 and 331, and 313 + 317 + 331 = 961 = 31^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A061275, A076304, A076305, A206280, A206281.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[50000]],3,1],IntegerQ[ Sqrt[ Total[#]]]&]][[1]]

PARI

p=2;q=3;forprime(r=5,1e9,if(issquare(p+q+r),print1(p", "));p=q;q=r) \\ Charles R Greathouse IV, Aug 28 2013

Formula

a(n) = A000040(A076305(n)). - Zak Seidov, Apr 07 2017