A084745 -id:A084745 - cp's OEIS frontend

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

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

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

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

Cf. A084745.

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);

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

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

A343589 Smallest prime of the form n^k-(n-1) or 0 if no such prime exists.

Original entry on oeis.org

3, 7, 13, 3121, 31, 43, 549755813881, 73, 991, 1321, 248821, 157, 2731, 211, 241, 34271896307617, 307, 6841, 13107199999999999999981, 421, 463, 141050039560662968926081, 331753, 601, 17551, 7625597484961, 757, 1816075630094014572464024421543167816955354437761

Offset: 2

Blake Branstool, Apr 20 2021

nonn

All values up to n=70 have been found and proved to be primes. n=71 has k=3019 and gives a probable prime.

See A113516, which gives the k values and is the main entry for these primes, for more extensively researched information. - Peter Munn, Nov 20 2021

			For n=2 and k=2, 2^2-(2-1)=3 thus a(2)=3. k is 2 as well for n=3,4.
For n=5 the first k to result in a prime is 5, 5^5-(5-1)=3121 thus a(5)=3121.

Blake Branstool, Table of n, a(n) for n = 2..70

A113516 gives the k values.

Cf. A076846, A084741, A084745, A346154.

a(n) = my(k=1, p); while (!isprime(p=n^k-(n-1)), k++); p; \\ Michel Marcus, Nov 17 2021

Name revised by Peter Munn, Nov 16 2021

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Extensions