A273042 Numbers k such that (28*10^k + 191)/3 is prime.

0, 1, 2, 3, 5, 6, 9, 10, 33, 49, 92, 109, 548, 757, 814, 1289, 1460, 1644, 2782, 6355, 8028, 9276, 9366, 9765, 12002, 12089, 14491, 16180, 29102, 30989, 151682, 183403, 190105, 253210

Offset

1,3

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

a(35) > 3*10^5.

Links

Table of n, a(n) for n=1..34.

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

Makoto Kamada, Search for 93w97.

Example

3 is in this sequence because (28*10^3 + 191)/3 = 9397 is prime.
Initial terms and associated primes:
a(1) = 0, 73;
a(2) = 1, 157:
a(3) = 2, 997;
a(4) = 3, 9397;
a(5) = 5, 933397, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(28*10^# + 191)/3] &]

Prog

(PARI) is(n)=ispseudoprime((28*10^n + 191)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A018278 A137809 A219035 * A014838 A026459 A026461

Adjacent sequences: A273039 A273040 A273041 * A273043 A273044 A273045

Keyword

nonn,more

Author

Robert Price, May 13 2016

Extensions

a(31)-a(33) from Robert Price, Feb 27 2020

a(34) from Robert Price, Jul 12 2023

Status

approved