

A267420


Integers k such that 19*(10^k)+1 is prime.


1



1, 2, 3, 11, 18, 25, 60, 71, 85, 168, 285, 627, 872, 1092, 1101, 1169, 1974, 2011, 2135, 2405, 10147, 14029, 16121, 17501, 46548
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OFFSET

1,2


COMMENTS

For k>0, numbers n such that the digits 19 followed by k1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
a(26) > 10^5.


LINKS

Table of n, a(n) for n=1..25.
Makoto Kamada, Factorization of nearrepdigitrelated numbers.
Makoto Kamada, Search for 190w1.


EXAMPLE

3 is in this sequence because 19*10^3 + 1 = 19001 is prime.
Initial terms and associated primes:
a(1) = 1, 191;
a(2) = 2, 1901;
a(3) = 3, 19001;
a(4) = 11, 1900000000001;
a(5) = 18, 19000000000000000001, etc.


MAPLE

select(k>isprime(19*(10^k)+1), [$1..3000]); # Muniru A Asiru, Oct 07 2018


MATHEMATICA

Select[Range[0, 100000], PrimeQ[19*10^# + 1] &]


PROG

(PARI) is(n) = ispseudoprime(19*(10^n) + 1); \\ Altug Alkan, Jan 15 2016
(PARI) lista(nn) = for(n=1, nn, if(isprime(19*(10^n) +1 ), print1(n, ", "))); \\ Altug Alkan, Jan 18 2016


CROSSREFS

Sequence in context: A263937 A263938 A263932 * A322422 A024861 A025101
Adjacent sequences: A267417 A267418 A267419 * A267421 A267422 A267423


KEYWORD

nonn,more


AUTHOR

Emre APARI, Jan 14 2016


EXTENSIONS

a(13)a(20) from Altug Alkan, Jan 18 2016
a(21)a(25) from Robert Price, Oct 07 2018


STATUS

approved



