A120946 Least positive k such that Z(n) + k is prime, where Z(n) = 1357986420*(10^(10*n)-1)/(10^10-1).

11, 29, 67, 179, 113, 53, 193, 143, 103, 173, 793, 181, 43, 263, 601, 839, 13, 331, 179, 167, 841, 59, 557, 359, 2437, 139, 113, 317, 109, 389, 551, 3517, 757, 187, 1327, 829, 401, 523, 811, 487, 563, 1909, 473, 703, 583, 2131, 1751

Offset

1,1

Comments

The majority of the decimal expansions of these (probable) primes have the pattern 13579864201357986420..., e.g. a(3)=67 and Z(3) + 67 = 135798642013579864201357986487. a(1001)=4637. Proof: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 1357986420*(10^(10*1001)-1)/(10^10-1)+4637 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Running N+1 test using discriminant 7, base 2+sqrt(7) 1357986420*(10^(10*1001)-1)/(10^10-1)+4637 is Fermat and Lucas PRP!

Links

Table of n, a(n) for n=1..47.

Crossrefs

Sequence in context: A340573 A043139 A043919 * A216296 A099909 A106881

Adjacent sequences: A120943 A120944 A120945 * A120947 A120948 A120949

Keyword

nonn,less

Author

Jason Earls, Aug 19 2006

Status

approved