A032448 Smallest prime == -1 modulo prime(n).

3, 2, 19, 13, 43, 103, 67, 37, 137, 173, 61, 73, 163, 257, 281, 211, 353, 487, 401, 283, 1021, 157, 331, 1423, 193, 1009, 617, 641, 653, 677, 761, 523, 547, 277, 1489, 1811, 313, 977, 1669, 691, 1789, 1447, 4201, 1543, 787, 397, 421, 1783, 907, 457

Offset: 1

Author

Reinhard Zumkeller, Jun 25 2003

Keywords

• nonn

Comments

It appears that a(n) <= prime(n)^2-1, where prime(n) = A000040(n) is the n-th prime; see A035095 for a related conjecture. If correct, this implies A006530(a(n)+1)=prime(n), which in turn implies that there are no duplicated values in the sequence.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A035095, A088732, A006530, A000040.

Programs

Haskell

a032448 n = head [q | q <- a000040_list, let p = a000040 n,
                      q `mod` p == p - 1]
-- Reinhard Zumkeller, Aug 08 2013

Mathematica

f[n_] := Block[{p = Prime@ n}, r = p - 1; While[ !PrimeQ@ r, r += p]; r]; Array[f, 50] (* Robert G. Wilson v, Jun 20 2014 *)

PARI

a(n) = {prn = prime(n); p = 2; while(p % prn != prn - 1, p = nextprime(p+1)); p;} \\ Michel Marcus, Aug 04 2013

Extensions

Edited by Franklin T. Adams-Watters, Jun 21 2010