A099017 - OEIS

%I #27 Jul 08 2021 03:14:54

%S 0,1,2,6,10,12,13,22,32,46,61,68,90,110,652,1608,1904,2003,3038,3086,

%T 9580,9698,10639,14461

%N Numbers k such that 4*10^k + 6*R_k + 1 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%C Also numbers k such that (14*10^k + 1)/3 is prime.

%C a(25) > 2*10^5. - _Robert Price_, Jul 11 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/4/46667.htm#prime">Prime numbers of the form 466...667</a>.

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

%F a(n) = A101731(n-1) + 1, for n>1.

%e n = 1, 2, 6 are members since 47, 467, 4666667 are primes.

%t Do[ If[ PrimeQ[(14*10^n + 1)/3], Print[n]], {n, 0, 10000}] (* _Robert G. Wilson v_, Jan 17 2005 *)

%Y Cf. A002275, A099005, A098959, A101731.

%K more,nonn

%O 1,3

%A Julien Peter Benney (jpbenney(AT)ftml.net), Nov 13 2004

%E a(15)-a(22) from _Robert G. Wilson v_, Jan 17 2005

%E a(23)-a(24) from Kamada data by _Robert Price_, Dec 08 2010

%E Prepended a(1)=0 by _Robert Price_, Jul 11 2015