A289942 Numbers k such that (85*10^k - 1)/3 is prime.

1, 2, 5, 9, 64, 69, 118, 377, 409, 616, 959, 1093, 1726, 3034, 5929, 8140, 11197, 15293, 15381, 27811, 58091, 63757, 72025, 83921, 122585, 139913, 166297, 256301

Offset

1,2

Comments

Numbers k such that the digits 28 followed by k occurrences of the digit 3 is prime (see Example section).

a(29) > 3*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 283w.

Example

2 is in this sequence because (85*10^2 - 1)/3 = 2833 is prime.
Initial terms and associated primes:
a(1) = 1, 283;
a(2) = 2, 2833;
a(3) = 5, 2833333;
a(4) = 9, 28333333333;
a(5) = 64, 283333333333333333333333333333333333333333333333333333333333333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(85*10^# - 1)/3] &]

Prog

(PARI) isok(k) = isprime((85*10^k - 1)/3); \\ Michel Marcus, Jul 16 2017

Crossrefs

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

Sequence in context: A109469 A334986 A185160 * A239899 A188948 A334295

Adjacent sequences: A289939 A289940 A289941 * A289943 A289944 A289945

Keyword

nonn,more,hard

Author

Robert Price, Jul 15 2017

Extensions

a(25)-a(27) from Robert Price, Feb 03 2020

a(28) from Robert Price, Jul 02 2023

Status

approved