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A002957 Numbers k such that 2*10^k - 1 is prime.

%I A002957 M0680 #49 Jan 17 2023 07:11:42
%S A002957 1,2,3,5,7,26,27,53,147,236,248,386,401,546,785,1325,1755,2906,3020,
%T A002957 5407,5697,5969,7517,15749,19233,38232,55347,1059002
%N A002957 Numbers k such that 2*10^k - 1 is prime.
%C A002957 Also numbers k such that 10^k + 9*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C A002957 Serge Batalov discovered that 1059002 belongs to this sequence but may not be the next term. - _Max Alekseyev_, Sep 30 2013
%C A002957 a(28) > 410000 (from Kamada data). - _Robert Price_, Oct 19 2014
%C A002957 Rytis Slatkevičius proved there are no undiscovered terms up to 1059002, so that term has now been added as a(28). - _Jeppe Stig Nielsen_, Jan 17 2023
%D A002957 H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Page 162.
%D A002957 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002957 C. R. Zarnke and H. C. Williams, Computer determination of some large primes, pp. 563-570 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 2, edited R. C. Mullin et al., 1971.
%H A002957 Chris K. Caldwell, Prime Pages, <a href="https://primes.utm.edu/primes/search.php?Description=%5E2*10%5E%25-1&amp;OnList=all&amp;Number=20&amp;Style=HTML">Search output 2*10^?-1</a>
%H A002957 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/19999.htm#prime">Prime numbers of the form 199...99</a>.
%H A002957 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>
%t A002957 Do[ If[ PrimeQ[ 2*10^n - 1], Print[n] ], {n, 1, 15000} ]
%o A002957 (PARI) for(n=1, 10^5, if(ispseudoprime(2*10^n-1), print1(n, ", "))) \\ _Felix Fröhlich_, Jun 23 2014
%K A002957 hard,nonn,more
%O A002957 1,2
%A A002957 _N. J. A. Sloane_, _Simon Plouffe_
%E A002957 Corrected and extended by _Robert G. Wilson v_, Feb 02 2001
%E A002957 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
%E A002957 a(28) from _Jeppe Stig Nielsen_, Jan 17 2023