A242384 Lesser of consecutive primes whose sum is of the form k*(k+2), for some integer k.

3, 11, 59, 139, 179, 311, 419, 541, 919, 1399, 1621, 2111, 3119, 5099, 6379, 8059, 8839, 9377, 15661, 16007, 16741, 17107, 21011, 21839, 23539, 24419, 28081, 30011, 31489, 33533, 35617, 37811, 39461, 41759, 44699, 45293, 60899, 68819, 71059, 78007, 83639, 84457, 86111

Offset: 1

Author

Antonio Roldán, May 12 2014

Keywords

• nonn

Examples

			311 is in the sequence because 311 is prime, nextprime(311)=313, and 311+313 = 624 = 24*(24+2).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A242383, A242385.

Programs

Mathematica

Select[Partition[Prime[Range[9000]],2,1],IntegerQ[Sqrt[1+Total[#]]-1]&] [[All,1]] (* Harvey P. Dale, May 15 2017 *)

PARI

{k=2;while(k<10^5,l=nextprime(k+1);if(issquare(k+l+1),print1(k,", "));k=l)}