A099006 - OEIS

%I #17 Jul 08 2021 03:14:49

%S 2,3,26,27,45,62,147,1277,1665,1979,2970,12773,17702,19128,22206,

%T 22386,25053

%N Numbers k such that 2*10^k + 5*R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (23*10^k + 13)/9 is prime.

%C a(18) > 10^5. - _Robert Price_, Feb 16 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/2/25557.htm#prime">Prime numbers of the form 255...557</a>.

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

%F a(n) = A101962(n) + 1.

%e n = 2, 3, 26, 27 are members since 257, 2557, 255555555555555555555555557 and

%e 2555555555555555555555555557 are primes.

%t Do[ If[ PrimeQ[(23*10^n + 13)/9], Print[n]], {n, 0, 10000}]

%Y Cf. A002275, A101962.

%K more,nonn

%O 1,1

%A Julien Peter Benney (jpbenney(AT)ftml.net), Nov 07 2004

%E a(8), a(9), a(10) & a(11) from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 17 2004

%E a(12)-a(17) from Kamada data by _Robert Price_, Dec 14 2010