A391395 Primes of the form (A002110(k) + A002110(k + 1)) / 2 - 1.

3, 17, 1259, 270269, 116396279, 103515091679, 313986271960080719, 3987804966219837013431179, 1164668352920931987761876342466557189, 141150686467724967796377879843703940661695849, 484356786477979939357984922968235281751492257310909570867909780039

Offset

1,1

Comments

Are there infinitely many primes q = (A002110(k) + A002110(k + 1)) / 2 - 1 such that q is the lesser of twin primes (A001359) ? The first such primes q in this sequence are {3, 17, 270269, 103515091679}.

Links

Table of n, a(n) for n=1..11.

Example

p = 17: (A002110(2) + A002110(3)) / 2 - 1 = (6 + 30) / 2 - 1 = 17, thus p = 17 is a term.

Mathematica

seq[max_] := With[{p = FoldList[Times, Prime[Range[max]]]}, Select[(Most[p] + Rest[p])/2 - 1, PrimeQ]]; seq[40] (* Amiram Eldar, Feb 09 2026 *)

Crossrefs

Cf. A000040, A001359, A002110.

Sequence in context: A362647 A225728 A351590 * A175984 A378860 A051710

Adjacent sequences: A391392 A391393 A391394 * A391396 A391397 A391398

Keyword

nonn

Author

Ctibor O. Zizka, Feb 09 2026

Status

approved