A284638 Numbers k such that (4*10^k + 149)/9 is prime.

0, 2, 3, 6, 12, 15, 17, 24, 26, 30, 156, 341, 519, 1284, 1455, 1841, 1874, 3410, 3890, 6185, 8472, 8696, 67784, 72174, 84779, 87669, 99693, 114296, 119474, 152253, 183659

Offset

1,2

Comments

For k > 1, numbers k such that k-2 occurrences of the digit 4 followed by the digits 61 is prime (see Example section).

a(32) > 2*10^5.

Links

Table of n, a(n) for n=1..31.

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

Makoto Kamada, Search for 4w61.

Example

3 is in this sequence because (4*10^3 + 149)/9 = 461 is prime.
Initial terms and associated primes:
a(1) = 0, 17;
a(2) = 2, 61;
a(3) = 3, 461;
a(4) = 6, 444461;
a(5) = 12, 444444444461; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(4*10^# + 149)/9] &]

Prog

(PARI) isok(k) = ispseudoprime((4*10^k + 149)/9); \\ Altug Alkan, Apr 12 2018

Crossrefs

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

Sequence in context: A291174 A281110 A252792 * A111271 A217647 A070926

Adjacent sequences: A284635 A284636 A284637 * A284639 A284640 A284641

Keyword

nonn,more,hard

Author

Robert Price, Mar 30 2017

Extensions

a(28)-a(31) from Robert Price, Apr 12 2018

Status

approved