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

1,1

Comments

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

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

Table of n, a(n) for n=1..19.

Patrick De Geest, PDP Reference Table - 757.

Makoto Kamada, Prime numbers of the form 755...557.

Index entries for primes involving repunits.

Formula

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

Example

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

Crossrefs

Cf. A082697-A082720, A056259.

Sequence in context: A247353 A293948 A281318 * A074710 A057460 A269112

Adjacent sequences: A082710 A082711 A082712 * A082714 A082715 A082716

Keyword

nonn,base,hard,more

Author

Patrick De Geest, Apr 13 2003

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

Status

approved