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A289051 Numbers k such that 13*10^k + 1 is prime. 1
1, 2, 3, 7, 16, 53, 95, 105, 125, 163, 358, 423, 562, 1774, 3459, 13957, 17962, 51179, 65963, 72808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For k>0, numbers such that the digits 13 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).

a(21) > 10^5.

LINKS

Table of n, a(n) for n=1..20.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 130w1.

EXAMPLE

2 is in this sequence because 13*10^3 + 1 = 1301 is prime.

Initial terms and primes associated:

a(1) = 1, 131;

a(2) = 2, 1301;

a(3) = 3, 13001;

a(4) = 7, 130000001;

a(5) = 16, 130000000000000001; etc.

MATHEMATICA

Select[Range[0, 100000], PrimeQ[13*10^# + 1] &]

CROSSREFS

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

Sequence in context: A246829 A296231 A089125 * A282320 A002854 A036356

Adjacent sequences:  A289048 A289049 A289050 * A289052 A289053 A289054

KEYWORD

nonn,more,hard

AUTHOR

Robert Price, Jun 22 2017

STATUS

approved

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Last modified November 15 21:17 EST 2019. Contains 329151 sequences. (Running on oeis4.)