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

1,2

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).

Links

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

Example

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

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 *)

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.

Sequence in context: A153195 A354884 A279097 * A010068 A295674 A120632

Adjacent sequences: A279095 A279096 A279097 * A279099 A279100 A279101

Keyword

nonn

Author

Jon E. Schoenfield, Mar 24 2017

Status

approved