Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 May 14 2024 20:17:21
%S 29,59,599,2999,8999,29999999
%N Primes of the form p = k*10^m - 1 where k is 3, 6 or 9, such that p+2 is also a prime.
%C There are no more terms for m <= 34936. - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 29 2007
%H M. Kamada, <a href="https://stdkmd.net/nrr/">Factorizations of near-repdigit numbers</a>
%e a(1)= because 3*10^1-1 = 29 and 3*10^1+1 = 31 are primes.
%e a(2)= because 6*10^1-1 = 59 and 6*10^1+1 = 61 are primes.
%e a(3)= because 6*10^2-1 = 599 and 6*10^2+1 = 601 are primes.
%e a(4)= because 3*10^3-1 = 2999 and 3*10^3+1 = 3001 are primes.
%e a(5)= because 9*10^3-1 = 8999 and 9*10^3+1 = 9001 are primes.
%e a(6)= because 3*10^7-1 = 29999999 and 3*10^7+1 = 30000001 are primes.
%t Select[FromDigits/@Flatten[Table[PadRight[{k},n,9],{k,{2,5,8}},{n,2,10}],1],AllTrue[ #+{0,2},PrimeQ]&]//Union (* _Harvey P. Dale_, May 14 2024 *)
%K more,nonn
%O 1,1
%A _Lekraj Beedassy_, Dec 21 2006
%E Edited by _N. J. A. Sloane_, Jan 01 2007