|
%I #33 Jan 17 2019 13:44:08
%S 1,2,3,11,18,25,60,71,85,168,285,627,872,1092,1101,1169,1974,2011,
%T 2135,2405,10147,14029,16121,17501,46548
%N Integers k such that 19*(10^k)+1 is prime.
%C For k>0, numbers n such that the digits 19 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
%C a(26) > 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 190w1.</a>
%e 3 is in this sequence because 19*10^3 + 1 = 19001 is prime.
%e Initial terms and associated primes:
%e a(1) = 1, 191;
%e a(2) = 2, 1901;
%e a(3) = 3, 19001;
%e a(4) = 11, 1900000000001;
%e a(5) = 18, 19000000000000000001, etc.
%p select(k->isprime(19*(10^k)+1),[$1..3000]); # _Muniru A Asiru_, Oct 07 2018
%t Select[Range[0, 100000], PrimeQ[19*10^# + 1] &]
%o (PARI) is(n) = ispseudoprime(19*(10^n) + 1); \\ _Altug Alkan_, Jan 15 2016
%o (PARI) lista(nn) = for(n=1, nn, if(isprime(19*(10^n) +1 ), print1(n, ", "))); \\ _Altug Alkan_, Jan 18 2016
%K nonn,more
%O 1,2
%A _Emre APARI_, Jan 14 2016
%E a(13)-a(20) from _Altug Alkan_, Jan 18 2016
%E a(21)-a(25) from _Robert Price_, Oct 07 2018
|
