A099190 - OEIS

%I #20 Aug 13 2020 14:01:06

%S 1,3,5,6,10,12,13,39,48,54,64,82,147,148,360,399,1638,1876,2146,2194,

%T 15789,23074,38466,68400

%N Numbers n such that 8*10^n-7 is prime.

%C Also numbers n such that 7*10^n + 9*R_n - 6 is prime, where R_n = 11...1 is the repunit (A002275) of length n.

%C Primes of the form 7*10^n+9R_n-6 are the only primes which are one more than twice their reversal.

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

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/79993.htm#prime">Prime numbers of the form 799...993</a>.

%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a>.

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

%F a(n) = A101155(n) + 1.

%e 73, 7993, 799993, 7999993, etc. are primes.

%t Do[ If[ PrimeQ[8*10^n - 7], Print[n]], {n, 10000}]

%o (PARI) is(n)=ispseudoprime(8*10^n-7) \\ _Charles R Greathouse IV_, Feb 20 2017

%Y Cf. A002275, A099181, A101155.

%K more,nonn

%O 1,2

%A _Robert G. Wilson v_, Oct 01 2004

%E a(19) & a(20) from _Robert G. Wilson v_, Jan 19 2005

%E a(21)-a(24) from Kamada data by _Robert Price_, Dec 14 2010