A076689 - OEIS

A076689

Smallest k such that k*prime(n)# + 1 is prime where prime(n)# is the n-th primorial number A002110(n).

1, 1, 1, 1, 1, 4, 8, 11, 4, 11, 1, 4, 7, 6, 14, 3, 5, 2, 7, 3, 6, 20, 2, 9, 20, 2, 5, 7, 31, 2, 12, 13, 24, 7, 39, 21, 35, 24, 22, 3, 21, 8, 9, 13, 39, 21, 29, 10, 3, 62, 52, 21, 3, 36, 28, 15, 18, 33, 7, 46, 33, 20, 14, 22, 41, 7, 27, 39, 20, 4, 4, 5, 15, 27, 1, 44, 99, 9, 52, 2, 27, 12

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OFFSET

1,6

COMMENTS

From Pierre CAMI, Sep 12 2017: (Start)

Conjectures:

lim_{N->infinity} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} n) = 1/2;

a(n)/n is always < 4.

This is certified for the first 3100 primes a(n)*prime(n)#+1.

(End)

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..3100

Pierre CAMI, PFGW Sript

MATHEMATICA

With[{P = FoldList[Times, Prime@ Range@ 120]}, Table[k = 1; While[CompositeQ[k P[[n]] + 1], k++]; k, {n, Length@ P}]] (* Michael De Vlieger, Sep 18 2017 *)

PROG

(PARI) a(n) = my(k=1, pr = prod(i=1, n, prime(i))); while (! isprime(k*pr+1), k++); k; \\ Michel Marcus, Oct 09 2017

CROSSREFS

Cf. A002110, A014545 (n for which k=1), A073917 (the primes).

Sequence in context: A131803 A133270 A131517 * A161867 A311011 A331052

Adjacent sequences: A076686 A076687 A076688 * A076690 A076691 A076692

KEYWORD

nonn

AUTHOR

Jason Earls, Nov 10 2002

STATUS

approved