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

1,1

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

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 *)

Prog

(PARI) a(n) = {prn = prime(n); p = 2; while(p % prn != prn - 1, p = nextprime(p+1)); p; } \\ Michel Marcus, Aug 04 2013
(Haskell)
a032448 n = head [q | q <- a000040_list, let p = a000040 n,
                      q `mod` p == p - 1]
-- Reinhard Zumkeller, Aug 08 2013

Crossrefs

Cf. A035095, A088732, A006530, A000040.

Sequence in context: A075568 A366377 A057026 * A066195 A090587 A094554

Adjacent sequences: A032445 A032446 A032447 * A032449 A032450 A032451

Keyword

nonn

Author

Reinhard Zumkeller, Jun 25 2003

Extensions

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

Status

approved