A062251 Take minimal prime q such that n(q+1)-1 is prime (A060324), that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; sequence gives values of p.

2, 5, 11, 11, 19, 17, 41, 23, 53, 29, 43, 47, 103, 41, 59, 47, 67, 53, 113, 59, 83, 131, 137, 71, 149, 103, 107, 83, 173, 89, 433, 127, 131, 101, 139, 107, 443, 113, 233, 239, 163, 167, 257, 131, 179, 137, 281, 191, 293, 149, 1019, 311, 211, 431, 439, 167, 227

Offset: 1

Author

N. J. A. Sloane, Jul 01 2001

Keywords

• nonn
• nice
• easy

Comments

A conjecture of Schinzel, if true, would imply that such a p always exists.

Examples

			1 = (2+1)/(2+1), 2 = (5+1)/(2+1), 3 = (11+1)/(3+1), 4 = (11+1)/(2+1), ...
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Matthew M. Conroy, A sequence related to a conjecture of Schinzel, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.
• Peter Luschny, Schinzel-Sierpinski conjecture and Calkin-Wilf tree.
• A. Schinzel and W. Sierpiński, Sur certaines hypothèses concernant les nombres premiers, Acta Arithmetica 4 (1958), 185-208; erratum 5 (1958) p. 259.

Crossrefs

Cf. A060424. Values of q are given in A060324.

Programs

Haskell

a062251 n = (a060324 n + 1) * n - 1 -- Reinhard Zumkeller, Aug 28 2014

Maple

a:= proc(n) local q;
       q:= 2;
       while not isprime(n*(q+1)-1) do
          q:= nextprime(q);
       od; n*(q+1)-1
    end:
seq(a(n), n=1..300);

Mathematica

a[n_] := (q = 2; While[ ! PrimeQ[n*(q+1)-1], q = NextPrime[q]]; n*(q+1)-1); Table[a[n], {n, 1, 57}] (* Jean-François Alcover, Feb 17 2012, after Maple *)

Formula

a(n) = (A060324(n) + 1) * n - 1. - Reinhard Zumkeller, Aug 28 2014

Extensions

More terms from Vladeta Jovovic, Jul 02 2001