A057856 Least k such that (n+1)^k + n^k is a prime.

1, 1, 1, 2, 1, 1, 2, 1, 1, 32, 1, 2, 4, 1, 1, 4, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 4

Offset

1,4

Comments

Note: k must be of the form 2^m (see A058064 for the m values).

Conjecture: For every pair of relatively prime numbers (x, y) there exist at least one number n=2^m and one prime number p such that p = x^n + y^n. This sequence shows one case of this conjecture where y = x + 1. - Tomas Xordan, Jun 02 2007

Links

Table of n, a(n) for n=1..27.

Example

a(101)=16 because 101^16 + 102^16 = 254536435001431070450581794495937.

Mathematica

Do[ k = 0; While[ !PrimeQ[ (n + 1)^(2^k) + n^(2^k) ], k++ ]; Print[ 2^k ], {n, 1, 60} ].

Prog

(PARI) a(n) = my(k=1); while (!isprime(p=(n+1)^k + n^k), k++); k; \\ Michel Marcus, Sep 16 2018

Crossrefs

Cf. A058064, A130536.

Sequence in context: A238904 A214501 A318665 * A117939 A321436 A276167

Adjacent sequences: A057853 A057854 A057855 * A057857 A057858 A057859

Keyword

nonn,hard

Author

Robert G. Wilson v, Nov 14 2000

Status

approved