A281407 Numbers k such that (292*10^k - 1)/3 is prime.

0, 2, 4, 9, 14, 20, 28, 33, 156, 285, 302, 1121, 1300, 2540, 3873, 4706, 5297, 7292, 11086, 15928, 16203, 17267, 17793, 19326, 32009, 67659

Offset

1,2

Comments

Numbers k such that the digits 97 followed by k occurrences of the digit 3 is prime (see Example section).

a(27) > 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 973w3.

Example

2 is in this sequence because (292*10^2 - 1)/3 = 9733 is prime.
Initial terms and associated primes:
a(1) = 0, 97;
a(2) = 2, 9733;
a(3) = 4, 973333;
a(4) = 9, 97333333333;
a(5) = 14, 9733333333333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(292*10^# - 1)/3] &]

Prog

(PARI) isok(n) = isprime((292*10^n - 1)/3); \\ Michel Marcus, Jan 21 2017

Crossrefs

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

Sequence in context: A234899 A190553 A270532 * A078671 A119637 A169762

Adjacent sequences: A281404 A281405 A281406 * A281408 A281409 A281410

Keyword

nonn,more,hard

Author

Robert Price, Jan 21 2017

Status

approved