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A279099 Numbers k such that prime(k) divides primorial(j) + 1 for exactly two integers j. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A255352 A044391 A044772 * A142799 A250025 A140626

Adjacent sequences:  A279096 A279097 A279098 * A279100 A279101 A279102

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Mar 24 2017

STATUS

approved

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Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)