A280017 Numbers k such that (10^k - 13)/3 is prime.

2, 4, 5, 8, 11, 25, 35, 270, 401, 613, 635, 768, 1283, 2941, 3409, 4266, 4391, 10744, 22979, 26766, 27743, 35514, 59174, 86906, 99239, 154494

Offset

1,1

Comments

For k > 1, numbers such that k - 2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section).

a(27) > 2 * 10^5. - Price

There are no odd multiples of 3 in this sequence. If k is an odd multiple of 3, then (10^k - 13)/3 is divisible by 7. The smallest even multiple of 3 in the sequence is 270. - Alonso del Arte, Dec 31 2017

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 3w29.

Example

4 is in this sequence because (10^4 - 13)/3 = 3329 is prime.
Here is a listing of the initial terms and associated primes:
a(1) = 2, 29;
a(2) = 4, 3329;
a(3) = 5, 33329;
a(4) = 8, 33333329;
a(5) = 11, 33333333329; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[(10^# - 13)/3] &]

Prog

(PARI) isok(n) = isprime((10^n-13)/3); \\ Altug Alkan, Dec 31 2017

Crossrefs

Cf. A056707 (numerators of (10^k - 13)/3 that are prime for k negative), A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A288523 A240179 A295032 * A080136 A080033 A007379

Adjacent sequences: A280014 A280015 A280016 * A280018 A280019 A280020

Keyword

nonn,more,hard

Author

Robert Price, Feb 21 2017

Extensions

a(26) from Robert Price, Dec 31 2017

Status

approved