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A084746
Smallest k such that n^k - k is a prime, or 0 if no such number exists.
3
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
2,1
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).
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}]
CROSSREFS
Cf. A084745.
Sequence in context: A230798 A266224 A029396 * A128259 A051194 A134838
KEYWORD
more,nonn,hard
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003
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
STATUS
approved