A295030 - OEIS

%I #19 May 11 2024 19:36:59

%S 1,2,3,8,10,15,31,32,77,106,191,197,525,557,1958,3848,12771,13348,

%T 13507,23164,55932,67375,68020,95407,95672,109142,113905,150577,

%U 185905,261248

%N Numbers k such that 4*10^k + 91 is prime.

%C For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 91 is prime (see Example section).

%C a(31) > 3*10^5.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 40w91</a>.

%e 2 is in this sequence because 4*10^2 + 91 = 491 is prime.

%e Initial terms and associated primes:

%e a(1) = 1, 131;

%e a(2) = 2, 491;

%e a(3) = 3, 4091;

%e a(4) = 8, 400000091;

%e a(5) = 10, 40000000091; etc.

%t Select[Range[0, 100000], PrimeQ[4*10^# + 91] &]

%o (PARI) isok(k) = isprime(4*10^k + 91); \\ _Michel Marcus_, Nov 13 2017

%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

%K nonn,more,hard

%O 1,2

%A _Robert Price_, Nov 12 2017

%E a(26)-a(29) from _Robert Price_, Aug 18 2018

%E a(30) from _Robert Price_, Jun 01 2023