A242385 Lesser of consecutive primes whose average is of the form k*(k+2), for some integer k.

13, 97, 113, 193, 283, 397, 479, 673, 953, 1439, 1597, 2297, 2699, 3469, 4219, 4483, 5323, 7219, 8273, 9209, 9403, 10799, 12097, 13219, 14879, 15373, 15619, 21313, 23399, 26237, 27883, 32029, 32749, 34217, 37243, 39989, 41203, 42433, 43669, 46219, 55219, 60509, 62497

Offset: 1

Author

Antonio Roldán, May 12 2014

Keywords

• nonn

Examples

			193 is in the sequence because 193 is prime, nextprime(193) = 197, and (193+197)/2 = 195 = 13*(13+2).
		

Crossrefs

Cf. A242384.

Programs

Mathematica

Select[Partition[Prime[Range[6500]],2,1],IntegerQ[SolveValues[(k(k+2)) == Mean[#],k][[2]]]&][[All,1]] (* Harvey P. Dale, Mar 05 2022 *)

PARI

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