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A076689 Smallest k such that k*prime(n)# + 1 is prime where prime(n)# is the n-th primorial number A002110(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

From Pierre CAMI, Sep 12 2017: (Start)

Conjectures:

lim_{N->inf} (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. 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

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Last modified May 16 11:54 EDT 2021. Contains 343942 sequences. (Running on oeis4.)