A121521 Least positive k such that (10^n+1)^n + k is prime.

1, 2, 10, 2, 16, 12, 220, 60, 112, 222, 112, 30, 618, 348, 156, 248, 10, 290, 256, 2346, 118, 570, 738, 348, 1356, 4352, 1402, 470, 736, 300, 10428, 4962, 4882, 1382, 580, 948, 5112, 776, 358, 7158, 1458, 21056, 318, 4376, 2472, 2738, 9178, 2538, 10518, 4908, 11316

Offset: 0

Author

Jason Earls, Aug 05 2006

Keywords

• nonn

Comments

The 100th term is 16456; ((10^100+1)^100)+16456 is a probable prime with 10001 digits.

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..101

Crossrefs

Cf. A121520.

Programs

Mathematica

lpk[n_]:=Module[{c=(10^n+1)^n},NextPrime[c]-c]; Array[lpk,40,0] (* Harvey P. Dale, Sep 04 2017 *)

PARI

a(n) = nextprime(1+m=(10^n+1)^n) - m; \\ Jinyuan Wang, Jun 07 2020

Extensions

a(39)-a(46) from Jinyuan Wang, Jun 07 2020

a(47) and beyond from Michael S. Branicky, May 22 2023