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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
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
Sequence in context: A012988 A261535 A327020 * A062635 A060835 A122054
KEYWORD
nice,nonn,more
AUTHOR
Carlos Rivera, Dec 01 2000
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)