A058233
Primes p such that p#+1 is divisible by the next prime after p.
Original entry on oeis.org
2, 17, 1459, 2999
Offset: 1
2*3*5*7*11*13*17+1 is divisible by 19.
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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 *)
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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
A081618
Numbers n such that (product of first n primes)+1 is divisible by the (n+1)-th prime. Also n such that A075306(n)-1 is equal to A002110(n). Positions of 1 in A081617.
Original entry on oeis.org
The 8th prime, 19, divides 2*3*5*7*11*13*17+1=510511, thus 7 is a member.
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With[{nn=500},Flatten[Position[Thread[{Rest[FoldList[Times,1,Prime[ Range[ nn]]]]+ 1, Prime[ Range[2,nn+1]]}],?(Divisible[#[[1]],#[[2]]]&),{1},Heads->False]]] (* _Harvey P. Dale, Apr 18 2015 *)
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p=1; for(n=1, 10^5, p=p*prime(n); if((p+1)%prime(n+1)==0, print1(n", ")))
A341804
Primes p dividing (the product of the primes less than p)-1.
Original entry on oeis.org
2, 5, 11, 176078293
Offset: 1
The prime 11 is included because 2*3*5*7-1 is divisible by 11. Therefore, the last factor of the product, namely 7, is in A341812.
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t=1;forprime(p=2,,((t-1)%p==0)&&print1(p,", ");t*=p)
A100465
Let p(1)=2, p(2)=3, p(3)=5, ... denote the primes and let E(n) = 1 + p(1) * p(2) * ... * p(n). Sequence gives primes p such that p(n+2) | E(n).
Original entry on oeis.org
7, 271, 307, 673
Offset: 1
Lévai Gábor (gablevai(AT)vipmail.hu), Nov 23 2004
7 is a term of the sequence, because it is the 4th prime and divides E(2)=2*3+1=7 trivially. - _Martin Ehrenstein_, Feb 05 2021
See
A066735 for further information.
Showing 1-4 of 4 results.
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