

A290476


Numbers k such that (38*10^k + 691)/9 is prime.


0



2, 4, 8, 10, 14, 16, 29, 106, 179, 197, 365, 371, 557, 857, 862, 1163, 1454, 2206, 5075, 22384, 149999, 196792
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OFFSET

1,1


COMMENTS

For k > 1, numbers such that the digit 4 followed by k  2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).
There are no multiples of 3 in the sequence, since (38 * 10^k + 691)/9 is a multiple of 3 if k is.
a(23) > 2*10^5.


LINKS

Table of n, a(n) for n=1..22.
Makoto Kamada, Factorization of nearrepdigitrelated numbers.
Makoto Kamada, Search for 42w99.


EXAMPLE

4 is in this sequence because (38*10^4 + 691)/9 = 42299 is prime.
Initial terms and primes associated:
a(1) = 2, 499;
a(2) = 4, 42299;
a(3) = 8, 422222299;
a(4) = 10; 42222222299;
a(5) = 14, 422222222222299; etc.


MATHEMATICA

Select[Range[1000], PrimeQ[(38*10^# + 691)/9] &]


CROSSREFS

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
Sequence in context: A125499 A240092 A153974 * A189670 A034822 A300781
Adjacent sequences: A290473 A290474 A290475 * A290477 A290478 A290479


KEYWORD

nonn,more,hard


AUTHOR

Robert Price, Aug 03 2017


EXTENSIONS

a(21)a(22) from Robert Price, Oct 31 2018


STATUS

approved



