A295969 Numbers k such that (5*10^k - 473)/9 is prime.

2, 3, 4, 9, 10, 16, 27, 46, 97, 103, 214, 229, 241, 285, 643, 999, 3154, 14115, 43012, 85855, 87622, 87712, 90142, 168379

Offset

1,1

Comments

For k > 1, numbers k such that k-2 occurrences of the digit 5 followed by the digits 03 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 5w03.

Example

3 is in this sequence because (5*10^3 - 473)/9 = 503 is prime.
Initial terms and associated primes:
a(1) = 2, 3;
a(2) = 3, 503;
a(3) = 4, 5503;
a(4) = 9, 555555503;
a(5) = 10, 5555555503; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(5*10^# - 473)/9] &]

Prog

(PARI) isok(k) = isprime((5*10^k - 473)/9); \\ Michel Marcus, Dec 01 2017

Crossrefs

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

Sequence in context: A249943 A251620 A128944 * A174437 A127150 A256189

Adjacent sequences: A295966 A295967 A295968 * A295970 A295971 A295972

Keyword

nonn,more,hard

Author

Robert Price, Nov 30 2017

Extensions

a(24) from Robert Price, Jan 21 2018

Status

approved