A084746 Smallest k such that n^k - k is a prime, or 0 if no such number exists.

2, 1, 1, 2, 1, 2, 1, 2, 3, 18, 1, 2, 1, 2, 3, 6, 1, 2, 1, 2, 41, 110, 1, 18, 3, 2, 11, 2, 1, 24, 1, 2, 3, 2, 107827, 2, 1, 8, 3, 24, 1, 2, 1, 514, 6737, 2, 1, 2, 5521, 140, 15, 108, 1, 2, 15, 82, 35

Offset: 2

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003

Keywords

• more
• nonn
• hard

Comments

Conjecture: no entry is zero.

If n is odd and greater than 3, k=a(n) is even. If n is an even composite number, k=a(n) is odd. For n>2, n and k=a(n) are coprime. - R. J. Mathar, Apr 02 2006, corrected by Farideh Firoozbakht, Aug 09 2014

a(36)>30000 or 0. a(37)..a(46) = 2, 1, 8, 3, 24, 1, 2, 1, 514, 6737. - Max Alekseyev, Apr 24 2009

If n-1 is prime then a(n)=1. - Farideh Firoozbakht, Aug 09 2014

Links

• Henri Lifchitz & Renaud Lifchitz, 36^107827-107827, a(36).

Crossrefs

Cf. A084745.

Programs

Maple

a := proc(n) local k; k := 1; while not isprime(n^k-k) do k := k+1 od; k end: seq(a(n),n=2..35);

Mathematica

f[n_] := Block[{k = 1}, If[OddQ[n], k++ ]; While[ ! PrimeQ[n^k - k], k += 2]; k]; Table[ f[n], {n, 3, 35}]

Extensions

Edited and extended by Robert G. Wilson v, Alec Mihailovs (Alec(AT)Mihailovs.com) and T. D. Noe, Jun 16 2003

a(36)-a(58) from Kellen Shenton, Aug 14 2023