|
%I #22 Jun 01 2023 02:46:06
%S 1,2,4,5,7,9,10,17,21,41,51,59,61,77,79,83,97,108,427,615,869,900,966,
%T 3150,3239,3932,5218,11941,30558,44697,90334,113874,128343,142810,
%U 222253
%N Numbers k such that 4*10^k - 21 is prime.
%C For k>1, numbers that begin with the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 79 are prime (see Example section).
%C a(36) > 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/primedifficulty.txt">Search for 39w79.</a>
%e 4 is in this sequence because 4*10^4 - 21 = 39979; is prime.
%e Initial terms and primes associated:
%e a(1) = 1, 19;
%e a(2) = 2, 379;
%e a(3) = 4, 39979;
%e a(4) = 5, 399979;
%e a(5) = 7, 39999979, etc.
%t Select[Range[1, 100000], PrimeQ[4*10^# - 21] &]
%o (PARI) is(n)=ispseudoprime(4*10^n - 21) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K nonn,more
%O 1,2
%A _Robert Price_, Apr 17 2016
%E a(32)-a(34) from _Robert Price_, Sep 10 2018
%E a(35) from _Robert Price_, Jun 01 2023
|
