A295825 Numbers k such that (47*10^k + 493)/9 is prime.

1, 2, 7, 10, 16, 22, 32, 85, 106, 310, 374, 410, 421, 502, 850, 938, 1213, 2362, 4597, 50578, 59509, 77572, 136141, 174790

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 2 followed by the digits 77 is prime (see Example section).

a(25) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 52w77.

Example

2 is in this sequence because (47*10^2 + 493)/9 = 577 is prime.
Initial terms and associated primes:
a(1) = 1, 107;
a(2) = 2, 577;
a(3) = 7, 52222277;
a(4) = 10, 52222222277;
a(5) = 16, 52222222222222277; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(47*10^# + 493)/9] &]

Crossrefs

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

Sequence in context: A343990 A226830 A059316 * A140115 A294865 A105770

Adjacent sequences: A295822 A295823 A295824 * A295826 A295827 A295828

Keyword

nonn,more,hard

Author

Robert Price, Nov 28 2017

Extensions

a(23)-a(24) from Robert Price, Mar 23 2019

Status

approved