cp's OEIS Frontend

A257027 Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

%I A257027 #32 May 31 2024 22:11:52
%S A257027 0,2,3,9,11,18,74,131,144,161,224,282,390,398,614,791,1313,1866,9708,
%T A257027 10544,13292,13394,29703,30779,72446
%N A257027 Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
%C A257027 Also, numbers k such that (646*10^k - 7)/9 is prime.
%C A257027 Terms from Kamada.
%C A257027 a(26) > 10^5. _Robert Price_, Jul 31 2016
%H A257027 Makoto Kamada, <a href="https://stdkmd.net/nrr/">Factorization of near-repdigit-related numbers</a>.
%H A257027 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 717w</a>.
%H A257027 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%e A257027 For k=2, 7*R_4 - 6*10^2 = 7777 - 600 = 7177 which is prime.
%e A257027 a(1)=0 associated with 71, a(2)=2 associated with 7177, a(3)=3 associated with 71777, a(4)=9 associated with 71777777777, etc. - _Robert Price_, Jul 31 2016
%t A257027 Select[Range[0, 100000], PrimeQ[(646*10^#-7)/9 ] &]
%o A257027 (PARI) for(n=0,200,if(isprime((646*10^n-7)/9),print1(n,", "))) \\ _Derek Orr_, Apr 14 2015
%o A257027 (Magma) [n: n in [0..300] | IsPrime((646*10^n-7) div 9)]; // _Vincenzo Librandi_, Apr 15 2015
%Y A257027 Cf. A002275, A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A257027 more,hard,nonn
%O A257027 1,2
%A A257027 _Robert Price_, Apr 14 2015
%E A257027 a(25) from _Robert Price_, Jul 31 2016