A076846 -id:A076846 - cp's OEIS frontend

A076845 Least k>0 such that n^k + n - 1 is prime.

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 16, 1, 1, 4, 3, 1, 2, 1, 1, 4, 1, 3, 2, 1, 2, 10, 1, 1, 108, 3, 1, 2, 1, 1, 2, 2, 1, 2, 1, 3, 2, 1, 2, 20, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 2, 2, 7, 8, 3, 1, 2, 1, 24, 2, 1, 1, 12, 4, 3, 8, 1, 1, 4, 3, 1, 194, 3, 1, 2, 1, 2, 2, 1, 8, 2, 1, 1, 4, 2, 2, 54, 1, 1, 4, 1, 1

Offset: 2

Benoit Cloitre, Nov 20 2002

nonn

From Robert Israel, Apr 07 2025: (Start)
No terms == 5 (mod 6), as x^k + x - 1 is divisible by x^2 - x - 1 when k == 5 (mod 6).
a(113) > 7000 if it exists. (End)

Robert Israel, Incomplete table of n, a(n) for n = 2 .. 1000. -1 denotes a value that is > 3000 if it exists.

Cf. A078178, A076846.

Cf. A010051.

a076845 n = head [k | k <- [1..], a010051'' (n ^ k + n - 1) == 1]
-- Reinhard Zumkeller, Jul 17 2014

f:= proc(n) local k;
    for k from 1 do if isprime(n^k+n-1) then return k fi od
end proc:
map(f, [$2..112]); # Robert Israel, Apr 07 2025

lk[n_]:=Module[{k=1},While[!PrimeQ[n^k+n-1],k++];k]; Array[lk,100,2] (* Harvey P. Dale, Jun 29 2017 *)

a(n) = {my(k=1); while(!isprime(n^k+n-1), k++); k;} \\ Michel Marcus, Nov 29 2013

A078179 a(n) is the smallest prime of the form n^k + n - 1 with k >= 2.

Original entry on oeis.org

5, 11, 19, 29, 41, 349, 71, 89, 109, 131, 20747, 181, 2177953337809371149, 239, 271, 83537, 5849, 379, 419, 461, 2494357909, 279863, 599, 15649, 701, 19709, 811, 420707233300229, 929, 991

Offset: 2

Reinhard Zumkeller, Nov 20 2002

nonn

			349 = A000040(70) = 7^3+7-1 and 7^2+7-1 = 5*11, therefore a(7) = 349.

Reinhard Zumkeller, Table of n, a(n) for n = 2..100

Cf. A078178, A076846.

Cf. A010051, A002327.

a078179 n = n ^ (a078178 n) + n - 1  -- Reinhard Zumkeller, Jul 16 2014

a(n) = n^A078178(n) + n - 1.

More terms from Benoit Cloitre, Nov 20 2002

Offset corrected by Reinhard Zumkeller, Jul 16 2014

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

A076845 Least k>0 such that n^k + n - 1 is prime.

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A078179 a(n) is the smallest prime of the form n^k + n - 1 with k >= 2.

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

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions