A103356 a(n) is the least k such that k*((prime(n)#)^2)-1 is prime, where prime(n)# is the n-th primorial.

1, 2, 3, 3, 6, 2, 13, 13, 5, 6, 2, 11, 14, 15, 3, 7, 77, 6, 20, 41, 52, 6, 13, 8, 41, 52, 24, 26, 31, 41, 6, 31, 21, 28, 43, 57, 11, 18, 47, 19, 8, 33, 24, 30, 43, 10, 17, 213, 29, 15, 45, 60, 50, 26, 48, 18, 18, 78, 8, 59, 13, 33, 145, 23, 154, 79, 65, 21, 18, 23, 30, 19, 159, 46, 45

Offset

1,2

Links

Table of n, a(n) for n=1..75.

Example

1*2^2-1 = 3 prime, so a(1) = 1.
1*((2*3)^2)-1 = 35 is composite, 2*((2*3)^2)-1 = 71 is prime, so a(2) = 2.
1*((2*3*5)^2)-1 = 899 is composite, 2*((2*3*5)^2)-1 = 1799 is composite, 3*((2*3*5)^2)-1 = 2699 is prime, so a(3) = 3.

Mathematica

a[n_] := Module[{k = 1, s = Product[Prime[i], {i, 1, n}]^2}, While[!PrimeQ[k*s-1], k++]; k]; Array[a, 75] (* Amiram Eldar, Jul 18 2021 *)

Crossrefs

Cf. A002110.

Sequence in context: A323713 A054892 A104570 * A345385 A071915 A182578

Adjacent sequences: A103353 A103354 A103355 * A103357 A103358 A103359

Keyword

nonn

Author

Pierre CAMI, Mar 20 2005

Extensions

Data corrected by Amiram Eldar, Jul 18 2021

Status

approved