A302122 Numbers k such that 3*10^k + 29 is prime.

1, 4, 6, 16, 17, 22, 34, 40, 46, 67, 78, 457, 642, 1037, 1615, 3607, 6270, 10945, 12221, 27606, 27623, 49645, 136829, 180852

Offset

1,2

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 0 followed by the digits 29 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 30w29.

Example

4 is in this sequence because 3*10^4 + 29 = 30029 is prime.
Initial terms and associated primes:
a(1) = 1, 59;
a(2) = 4, 30029;
a(3) = 6, 3000029;
a(4) = 16, 30000000000000029;
a(5) = 17, 300000000000000029; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[3*10^# + 29] &]

Crossrefs

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

Sequence in context: A328965 A133092 A240034 * A056222 A186201 A138624

Adjacent sequences: A302119 A302120 A302121 * A302123 A302124 A302125

Keyword

nonn,more,hard,changed

Author

Robert Price, Apr 01 2018

Extensions

a(23)-a(24) from Robert Price, May 11 2018

a(14)-a(15) inserted from Kamada data by Tyler Busby, Apr 15 2024

Status

approved