A082713 Numbers k such that (68*10^(k-1) + 13)/9 is a depression prime.

3, 5, 11, 21, 23, 59, 75, 83, 209, 351, 423, 3813, 3983, 20925, 23787, 38853, 56043, 68505, 74435

Offset: 1

Author

Patrick De Geest, Apr 13 2003

Keywords

• nonn
• base
• hard
• more

Comments

Prime versus probable prime status and proofs are given in the De Geest link.

Examples

			k=21 -> (68*10^(21-1) + 13)/9 = 755555555555555555557.
		

References

• C. Caldwell and H. Dubner, The near repdigit primes A(n-k-1)B(1)A(k), especially 9(n-k-1)8(1)9(k), Journal of Recreational Mathematics, Volume 28, No. 1, 1996-97, pp. 1-9.

Links

• Patrick De Geest, PDP Reference Table - 757.
• Makoto Kamada, Prime numbers of the form 755...557.
• Index entries for primes involving repunits.

Crossrefs

Cf. A082697-A082720, A056259.

Formula

a(n) = A056259(n) + 2.

Extensions

Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(17)=56043 and a(18)=68505 from Ray Chandler, Nov 16 2010

a(19)=74434 from Ray Chandler, Nov 17 2010

a(19) corrected by Patrick De Geest, Nov 04 2014

Edited by Ray Chandler, Nov 05 2014

Definition rewritten by Michel Marcus, Oct 27 2019