A286177 Numbers k such that (17*10^k - 47)/3 is prime.

1, 3, 8, 9, 14, 17, 29, 43, 48, 72, 78, 132, 312, 894, 968, 5030, 5108, 9008, 11989, 12903, 26767, 28159, 30564, 39619, 44250, 54537, 77427

Offset

1,2

Comments

For k>1, numbers such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 51 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 56w51.

Example

3 is in this sequence because (17*10^3 - 47)/3 = 5651 is prime.
Initial terms and primes associated:
a(1) = 1, 41;
a(2) = 3, 5651;
a(3) = 8, 566666651;
a(4) = 9, 5666666651;
a(5) = 14, 566666666666651; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(17*10^# - 47)/3] &]

Crossrefs

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

Sequence in context: A259850 A071677 A084747 * A287579 A289142 A101065

Adjacent sequences: A286174 A286175 A286176 * A286178 A286179 A286180

Keyword

nonn,more,hard

Author

Robert Price, May 03 2017

Status

approved