A290878 Numbers k such that 4*10^k + 49 is prime.

0, 1, 2, 3, 8, 18, 20, 24, 40, 57, 84, 92, 111, 135, 138, 272, 423, 540, 542, 1147, 1246, 1713, 2217, 2767, 3486, 30586, 34183, 61119, 113658, 194668

Offset

1,3

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 49 is prime (see Example section).

a(31) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 40w49.

Example

3 is in this sequence because 4*10^3 + 49 = 4049 is prime.
Initial terms and associated primes:
a(1) = 0, 53;
a(2) = 1, 89;
a(3) = 2, 449;
a(4) = 3; 4049;
a(5) = 8, 400000049; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[4*10^# + 49] &]

Prog

(PARI) isok(k) = ispseudoprime(4*10^k + 49) \\ Altug Alkan, Aug 13 2017

Crossrefs

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

Sequence in context: A218090 A101182 A009207 * A096254 A091765 A368882

Adjacent sequences: A290875 A290876 A290877 * A290879 A290880 A290881

Keyword

nonn,more,hard

Author

Robert Price, Aug 13 2017

Extensions

a(29)-a(30) from Robert Price, Jan 21 2019

Status

approved