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A293272 Numbers k such that (10^k - 19)/9 is prime. 0
3, 4, 6, 9, 34, 36, 126, 141, 160, 286, 678, 1236, 3757, 4681, 4881, 6360, 6588, 7056, 7752, 41925, 43423, 43503, 47565, 52608, 55084, 76069, 199248 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For k > 1, numbers such that k-2 occurrences of the digit 1 followed by the digits 09 is prime (see Example section).

a(28) > 2*10^5.

LINKS

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 1w09

EXAMPLE

4 is in this sequence because (10^4 - 19)/9 = 1109 is prime.

Initial terms and primes associated:

a(1) = 3, 109;

a(2) = 4, 1109;

a(3) = 6, 111109;

a(4) = 9, 111111109;

a(5) = 34, 1111111111111111111111111111111109; etc.

MATHEMATICA

Select[Range[2, 100000], PrimeQ[10^# - 19)/9] &]

CROSSREFS

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

Sequence in context: A102934 A338061 A191699 * A192286 A242028 A254002

Adjacent sequences:  A293269 A293270 A293271 * A293273 A293274 A293275

KEYWORD

nonn,more,hard

AUTHOR

Robert Price, Oct 06 2017

EXTENSIONS

a(27) from Robert Price, Jan 02 2018

STATUS

approved

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Last modified April 13 00:24 EDT 2021. Contains 342934 sequences. (Running on oeis4.)