A291606 Numbers k such that 44*10^k + 3 is prime.

0, 1, 6, 7, 27, 51, 67, 69, 115, 153, 346, 351, 1152, 1807, 2508, 4470, 4875, 5277, 7527, 10339, 11407, 21807, 26199, 46473, 68368, 181029

Offset

1,3

Comments

For k>0, numbers such that the digits 44 followed by k-1 occurrences of the digit 0 followed by the digit 3 is prime (see Example section).

a(29) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 440w3.

Example

1 is in this sequence because 44*10^1 + 3 = 443 is prime.
Initial terms and primes associated:
a(1) = 0, 47;
a(2) = 1, 443;
a(3) = 6, 44000003;
a(4) = 7, 440000003;
a(5) = 27, 44000000000000000000000000003; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[44*10^# + 3] &]

Prog

(PARI) isok(k) = ispseudoprime(44*10^k + 3) \\ Altug Alkan, Aug 27 2017

Crossrefs

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

Sequence in context: A054289 A041078 A067229 * A041535 A129214 A042419

Adjacent sequences: A291603 A291604 A291605 * A291607 A291608 A291609

Keyword

nonn,more,hard

Author

Robert Price, Aug 27 2017

Extensions

a(28) from Robert Price, Apr 09 2020

Status

approved