A273907 Numbers k such that 2*10^k - 87 is prime.

2, 3, 4, 9, 10, 13, 15, 24, 26, 38, 39, 42, 433, 489, 495, 513, 597, 829, 2019, 2738, 3096, 3691, 5437, 7537, 8536, 34125, 40105, 41790, 52713, 104811, 173809, 175860

Offset

1,1

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 13 is prime (see Example section).

a(33) > 2*10^5.

Links

Table of n, a(n) for n=1..32.

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

Makoto Kamada, Search for 19w13.

Example

3 is in this sequence because 2*10^3 - 87 = 1913 is prime.
Initial terms and associated primes:
a(1) = 2, 113;
a(2) = 3, 1913;
a(3) = 4, 19913;
a(4) = 9, 1999999913;
a(5) = 10, 19999999913, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[2*10^# - 87] &]

Prog

(PARI) is(n)=ispseudoprime(2*10^n - 87) \\ Charles R Greathouse IV, Jun 08 2016

Crossrefs

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

Sequence in context: A200260 A190119 A357056 * A066105 A083180 A098551

Adjacent sequences: A273904 A273905 A273906 * A273908 A273909 A273910

Keyword

nonn,more

Author

Robert Price, Jun 03 2016

Extensions

a(30)-a(32) from Robert Price, Apr 13 2018

Status

approved