A294122 Numbers k such that 3*10^k + 37 is prime.

1, 2, 3, 7, 9, 15, 18, 23, 39, 147, 1104, 1158, 1466, 1514, 1935, 2149, 2203, 2553, 2730, 7169, 9807, 17684, 23828, 25824, 27207, 55679, 94964, 122977, 206927

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 37 is prime (see Example section).

a(30) > 3*10^5.

Links

Table of n, a(n) for n=1..29.

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

Makoto Kamada, Search for 30w37

Example

2 is in this sequence because 3*10^2 + 37 = 337 is prime.
Initial terms and primes associated:
a(1) = 1, 67;
a(2) = 2, 337;
a(3) = 3, 3037;
a(4) = 7, 30000037;
a(5) = 9, 3000000037; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[3*10^# + 37] &]

Crossrefs

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

Sequence in context: A019312 A135369 A294283 * A211539 A109660 A236544

Adjacent sequences: A294119 A294120 A294121 * A294123 A294124 A294125

Keyword

nonn,more,hard

Author

Robert Price, Oct 23 2017

Extensions

a(28) from Robert Price, Aug 15 2018

a(29) from Robert Price, Oct 26 2023

Status

approved