A090185 Least k such that k*p(n)# + p(n+1) is prime, where p(i)# denotes i-th primorial and p(i) denotes i-th prime.

1, 1, 1, 2, 6, 1, 1, 1, 2, 8, 3, 3, 8, 1, 2, 1, 1, 5, 12, 10, 1, 2, 18, 4, 3, 4, 14, 26, 2, 7, 38, 3, 15, 13, 8, 23, 42, 6, 45, 12, 5, 11, 26, 2, 3, 2, 16, 9, 7, 21, 39, 21, 76, 2, 18, 16, 42, 37, 6, 23, 10, 8, 51, 28, 33, 8, 94, 22, 4, 2, 11, 53, 1, 53, 10, 3, 10, 97, 19, 25, 4, 4, 15, 38, 70

Offset

1,4

Comments

k*p(n)# + p(n+1) is the least prime > k*p(n)# + p(n+1)+1 and if k*p(n)# + p(n+1)+1 is not prime it is the least prime > k*p(n)# + p(n+1).

Links

Table of n, a(n) for n=1..85.

Example

6 is the least k for n = 5 because 6*p(5)# + p(6) = 6*2*3*5*7*11+13 = 13873.

Mathematica

A002110[n_] := Product[Prime[i], {i, n}]; a[n_]:=Module[{k=1}, While[!PrimeQ[k*A002110[n]+Prime[n+1]], k++]; k]; Array[a, 85] (* Stefano Spezia, Aug 14 2024 *)

Crossrefs

Cf. A000040, A002110.

Sequence in context: A127508 A375348 A244814 * A059813 A097099 A316622

Adjacent sequences: A090182 A090183 A090184 * A090186 A090187 A090188

Keyword

base,nonn

Author

Pierre CAMI, Jan 21 2004

Status

approved