A357517 Primes that are the average of two consecutive primorial numbers A002110 plus one.

5, 19, 270271, 5105101, 103515091681, 3810649312471, 155835500831011, 313986271960080721, 282899575838889614011647241, 113405858671385228324474555982803921209616373612841704311161, 2900763693484834576932132901212043025388720793126978148639249341

Offset: 1

Author

Nicholas Leonard, Oct 01 2022

Keywords

• nonn

Comments

a(n) ends with digit 1, for n > 2.

Examples

			19 is a term since primorials A002110(2) = 6 and A002110(3) = 30 which give (6 + 30)/2 + 1 = 19 which is prime.
		

Crossrefs

Cf. A002110, A276939.

Programs

Mathematica

primorial[n_] := Times@@Table[Prime[k], {k, 1, n}];  Table[If[PrimeQ[(primorial[n] + primorial[n+1])/2 + 1], (primorial[n] + primorial[n+1])/2 + 1, Nothing], {n, 1, 40}]