A295972 Numbers k such that (49*10^k - 139)/9 is prime.

5, 6, 18, 27, 48, 51, 92, 396, 678, 1259, 2085, 2820, 3009, 4311, 5015, 7775, 7955, 8595, 120380, 166721

Offset

1,1

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 29 is prime (see Example section).

a(21) > 2*10^5.

Links

Table of n, a(n) for n=1..20.

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

Makoto Kamada, Search for 54w29.

Example

5 is in this sequence because (49*10^5 - 139)/9 = 544429 is prime.
Initial terms and associated primes:
a(1) = 5, 544429;
a(2) = 6, 5444429;
a(3) = 18, 5444444444444444429;
a(4) = 27, 5444444444444444444444444429; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(49*10^# - 139)/9] &]

Prog

(PARI) isok(k) = isprime((49*10^k - 139)/9); \\ Michel Marcus, Dec 01 2017

Crossrefs

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

Sequence in context: A180134 A192727 A056519 * A333405 A063445 A257331

Adjacent sequences: A295969 A295970 A295971 * A295973 A295974 A295975

Keyword

nonn,more,hard

Author

Robert Price, Nov 30 2017

Extensions

a(19)-a(20) from Robert Price, Mar 04 2019

Status

approved