A278442 Numbers k such that (11*10^k - 179) / 3 is prime.

2, 3, 4, 5, 7, 14, 16, 47, 68, 103, 127, 341, 523, 562, 1259, 2206, 3164, 3335, 5450, 7700, 7822, 8902, 23237, 36431, 39874, 123899, 129239

Offset

1,1

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 07 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 36w07.

Example

4 is in this sequence because (11*10^4 - 179) / 3 = 36607 is prime.
Initial terms and associated primes:
a(1) = 2, 307;
a(2) = 3, 3607;
a(3) = 4, 36607;
a(4) = 5, 366607;
a(5) = 7, 36666607; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(11*10^# - 179) / 3] &]

Prog

(Magma) [n: n in [2..400] | IsPrime((11*10^n-179) div 3)]; // Vincenzo Librandi, Nov 23 2016
(PARI) is(n)=ispseudoprime((11*10^n - 179)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A337188 A125707 A039060 * A092065 A044955 A297136

Adjacent sequences: A278439 A278440 A278441 * A278443 A278444 A278445

Keyword

nonn,more,hard

Author

Robert Price, Nov 22 2016

Extensions

a(26)-a(27) from Robert Price, Sep 22 2018

Status

approved