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

1,1

Links

Table of n, a(n) for n=1..43.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A242384.

Sequence in context: A297081 A297603 A094499 * A141894 A275879 A160554

Adjacent sequences: A242382 A242383 A242384 * A242386 A242387 A242388

Keyword

nonn

Author

Antonio Roldán, May 12 2014

Status

approved