A125973 Smallest k such that k^n + k^(n-1) - 1 is prime.
2, 2, 2, 2, 2, 3, 2, 2, 14, 4, 7, 2, 38, 6, 7, 3, 4, 10, 2, 9, 74, 6, 10, 7, 4, 61, 20, 4, 5, 9, 6, 16, 6, 8, 2, 9, 4, 10, 2, 48, 44, 163, 9, 2, 95, 3, 27, 70, 6, 26, 57, 9, 6, 8, 207, 2, 27, 15, 45, 7, 69, 199, 55, 16, 2, 5, 12, 43, 137, 39, 9, 57, 5, 20, 4, 115, 2, 103, 45, 15, 20, 109
Offset: 1
Keywords
Examples
Consider n = 6. k^6 + k^5 - 1 evaluates to 1, 95, 971 for k = 1, 2, 3. Only the last of these numbers is prime, hence a(6) = 3.
Links
- Robert Israel, Table of n, a(n) for n = 1..800
- W. Ljunggren, On the irreducibility of certain trinomials and quadrinomials, Math. Scand. 8 (1960) 65-70.
- Wikipedia, Bunyakovsky conjecture.
Crossrefs
Programs
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Maple
f:= proc(n) local k; for k from 2 do if isprime(k^n+k^(n-1)-1) then return k fi od end proc: map(f, [$1..100]); # Robert Israel, Nov 16 2016
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Mathematica
a[n_] := For[k = 2, True, k++, If[PrimeQ[k^n + k^(n-1) - 1], Return[k]]]; Array[a, 100] (* Jean-François Alcover, Feb 26 2019 *)
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PARI
{m=82;for(n=1,m,k=1;while(!isprime(k^n+k^(n-1)-1),k++);print1(k,","))} \\ Klaus Brockhaus, Dec 17 2006
Extensions
Edited and extended by Klaus Brockhaus, Dec 17 2006
Comments