A276114 Numbers k such that (101*10^k - 17)/3 is prime.

1, 2, 15, 17, 26, 41, 56, 59, 121, 137, 224, 506, 611, 836, 937, 1079, 1829, 2315, 2666, 2879, 6661, 7167, 14021, 15459, 32924, 73346, 176815, 177302

Offset

1,2

Comments

Numbers k such that the digits 33 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).

a(29) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 336w1.

Example

2 is in this sequence because (101*10^2 - 17)/3 = 3361 is prime.
Initial terms and associated primes:
a(1) = 1, 331;
a(2) = 2, 3361;
a(3) = 15, 33666666666666661;
a(4) = 17, 3366666666666666661;
a(5) = 26, 3366666666666666666666666661, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(101*10^# - 17)/3] &]

Prog

(PARI) is(n)=ispseudoprime((101*10^n  - 17)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A370977 A337824 A114606 * A022117 A042571 A041797

Adjacent sequences: A276111 A276112 A276113 * A276115 A276116 A276117

Keyword

nonn,more

Author

Robert Price, Aug 18 2016

Extensions

a(27)-a(28) from Robert Price, Feb 05 2020

Status

approved