A242384 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS