A082713 - OEIS

%I #31 Nov 10 2019 01:33:39

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

%T 68505,74435

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

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

%D 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.

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp757">PDP Reference Table - 757</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/75557.htm#prime">Prime numbers of the form 755...557</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

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

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

%Y Cf. A082697-A082720, A056259.

%K nonn,base,hard,more

%O 1,1

%A _Patrick De Geest_, Apr 13 2003

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

%E a(17)=56043 and a(18)=68505 from _Ray Chandler_, Nov 16 2010

%E a(19)=74434 from _Ray Chandler_, Nov 17 2010

%E a(19) corrected by _Patrick De Geest_, Nov 04 2014

%E Edited by _Ray Chandler_, Nov 05 2014

%E Definition rewritten by _Michel Marcus_, Oct 27 2019