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

1,1

Comments

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

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.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A300677 A079008 A144573 * A091114 A155767 A079782

Adjacent sequences: A062248 A062249 A062250 * A062252 A062253 A062254

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Jul 01 2001

Extensions

More terms from Vladeta Jovovic, Jul 02 2001

Status

approved