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.

1, 7, 232, 430

Offset

1,2

Comments

a(5) is greater than 10^7. - Matty Muir, Oct 01 2020

Links

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

Example

The 8th prime, 19, divides 2*3*5*7*11*13*17+1=510511, thus 7 is a member.

Mathematica

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 *)

Prog

(PARI) p=1; for(n=1, 10^5, p=p*prime(n); if((p+1)%prime(n+1)==0, print1(n", ")))

Crossrefs

Cf. A066735.

Sequence in context: A343128 A142116 A201955 * A285369 A287042 A160491

Adjacent sequences: A081615 A081616 A081617 * A081619 A081620 A081621

Keyword

nonn,hard,more

Author

Ralf Stephan, Mar 24 2003

Status

approved