A279098 Numbers k such that prime(k) divides primorial(j) + 1 for exactly one integer j.

1, 2, 4, 8, 11, 17, 18, 21, 25, 32, 34, 35, 39, 40, 42, 47, 48, 58, 63, 65, 66, 67, 69, 90, 91, 97, 105, 110, 122, 140, 144, 151, 152, 162, 166, 168, 173, 174, 175, 179, 180, 186, 205, 207, 208, 210, 211, 218, 233, 243, 249, 256, 261, 262, 297, 308, 316, 318

Offset: 1

Author

Jon E. Schoenfield, Mar 24 2017

Keywords

• nonn

Comments

As used here, "primorial(j)" refers to the product of the first j primes, i.e., A002110(j).

Primorial(j) + 1 is the j-th Euclid number, A006862(j).

Examples

			59 is not in this sequence because both primorial(7) + 1 = 510511 and primorial(17) + 1 = 1922760350154212639071 are divisible by prime(59) = 277.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A279097 (which also includes numbers k such that prime(k) divides primorial(j) + 1 for more than one integer j).

Cf. A000040, A002110, A006862, A113165, A279099, A283928.

Programs

Mathematica

np[1]=1; np[n_] := Block[{c=0, p=Prime[n], trg, x=1}, trg = p-1; Do[x = Mod[x Prime[k], p]; If[trg == x, c++], {k, n-1}]; c]; Select[Range[262], np[#] == 1 &] (* Giovanni Resta, Mar 29 2017 *)