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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 (list; graph; refs; listen; history; text; internal format)
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.

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

LINKS

Table of n, a(n) for n=2..35.

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

Adjacent sequences:  A084743 A084744 A084745 * A084747 A084748 A084749

KEYWORD

more,nonn

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

Update on a(36) and a(46) from Max Alekseyev, Apr 24 2009

STATUS

approved

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Last modified January 21 10:22 EST 2022. Contains 350476 sequences. (Running on oeis4.)