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A279097 Numbers k such that prime(k) divides primorial(j) + 1 for some j. 5
1, 2, 4, 8, 11, 17, 18, 21, 25, 32, 34, 35, 39, 40, 42, 47, 48, 58, 59, 63, 65, 66, 67, 69, 90, 91, 97, 105, 110, 122, 140, 144, 151, 152, 162, 166, 168, 173, 174, 175, 177, 179, 180, 186, 205, 207, 208, 210, 211, 218, 221, 233, 243, 249, 256, 260, 261, 262 (list; graph; refs; listen; history; text; internal format)
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

1 is in the sequence because primorial(0) + 1 = 1 + 1 = 2 is divisible by prime(1) = 2.

4 is in the sequence because primorial(2) + 1 = 2*3 + 1 = 7 is divisible by prime(4) = 7.

8 is in the sequence because primorial(7) + 1 = 2*3*5*7*11*13*17 + 1 = 510511 is divisible by prime(8) = 19.

59 is in the sequence because primorial(7) + 1 = 510511 is divisible by prime(59) = 277 (and primorial(17) + 1 = 1922760350154212639071 is divisible by prime(59) as well).

5 is not in the sequence because there is no number j such that primorial(j) + 1 is divisible by prime(5) = 11:

    primorial(1) + 1 = 2       + 1 =   3 == 3 (mod 11)

    primorial(2) + 1 = 2*3     + 1 =   7 == 7 (mod 11)

    primorial(3) + 1 = 2*3*5   + 1 =  31 == 9 (mod 11)

    primorial(4) + 1 = 2*3*5*7 + 1 = 211 == 2 (mod 11)

and primorial(j) + 1 = 2*...*11*... + 1  == 1 (mod 11) for all j >= 5.

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[#] > 0 &] (* Giovanni Resta, Mar 29 2017 *)

CROSSREFS

Cf. A000040, A002110, A006862, A113165, A279098, A279099, A283928.

Sequence in context: A018408 A018320 A153195 * A279098 A010068 A295674

Adjacent sequences:  A279094 A279095 A279096 * A279098 A279099 A279100

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Mar 24 2017

STATUS

approved

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Last modified January 18 14:04 EST 2020. Contains 331011 sequences. (Running on oeis4.)