A279099 Numbers k such that prime(k) divides primorial(j) + 1 for exactly two integers j.

59, 177, 221, 260, 285, 431, 476, 489, 625, 653, 686, 860, 957, 1320, 1334, 1734, 1987, 2140, 2215, 2854, 2991, 3051, 3341, 3455, 3535, 3591, 3645, 3695, 3798, 4020, 4032, 4079, 4612, 4614, 4856, 4904, 5019, 5234, 5263, 5842, 6178, 6184, 6491, 6639, 6745, 7151

Offset

1,1

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..5000

Example

59 is in this sequence because prime(59) = 277 divides primorial(j) + 1 for exactly two integers j: 7 and 17.
436 is not in this sequence because prime(436) = 3041 divides primorial(j) + 1 for exactly three integers j: 206, 263, and 409.

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[1000], np[#] == 2 &] (* Giovanni Resta, Mar 29 2017 *)

Crossrefs

Subsequence of A279097 (which includes all numbers k such that prime(k) divides primorial(j) + 1 for one or more integers j); cf. A279098 (exactly one integer j).

Cf. A000040, A002110, A006862, A113165, A279098, A283928.

Sequence in context: A044391 A044772 A341659 * A142799 A250025 A140626

Adjacent sequences: A279096 A279097 A279098 * A279100 A279101 A279102

Keyword

nonn

Author

Jon E. Schoenfield, Mar 24 2017

Status

approved