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A058233 Primes p such that p#+1 is divisible by the next prime after p. 8
2, 17, 1459, 2999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No additional terms through the 100000th prime. - Harvey P. Dale, Mar 12 2014

a(5) > prime(1400000) = 22182343. - Robert Price, Apr 02 2018

LINKS

Table of n, a(n) for n=1..4.

Carlos Rivera, Puzzle 117: Certain p#+1 values, The Prime Puzzles and Problems Connection.

EXAMPLE

2*3*5*7*11*13*17+1 is divisible by 19.

MATHEMATICA

primorial[n_] := Product[ Prime[k], {k, 1, PrimePi[n]}]; Select[ Prime[ Range[1000]], Divisible[ primorial[#] + 1, NextPrime[#]] &] (* Jean-François Alcover, Aug 19 2013 *)

Module[{prs=Prime[Range[500]]}, Transpose[Select[Thread[{Rest[ FoldList[ Times, 1, prs]], prs}], Divisible[ First[#]+1, NextPrime[Last[#]]]&]][[2]]] (* Harvey P. Dale, Mar 12 2014 *)

PROG

(Python)

from sympy import nextprime

A058233_list, p, q, r = [], 2, 3, 2

for _ in range(10**3):

if (r+1) % q == 0:

A058233_list.append(p)

r *= q

p, q = q, nextprime(q) # Chai Wah Wu, Sep 27 2021

CROSSREFS

Cf. A006862, A066735, A341804.

Sequence in context: A012988 A261535 A327020 * A062635 A060835 A122054

Adjacent sequences: A058230 A058231 A058232 * A058234 A058235 A058236

KEYWORD

nice,nonn,more

AUTHOR

Carlos Rivera, Dec 01 2000

STATUS

approved

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Last modified November 26 13:43 EST 2022. Contains 358362 sequences. (Running on oeis4.)