A276322 Numbers k such that (13*10^k + 83) / 3 is prime.

1, 2, 5, 7, 17, 18, 25, 60, 64, 66, 118, 125, 1021, 1901, 2273, 2524, 6048, 7098, 8281, 11634, 13843, 16098, 18652, 18661, 20570, 32291, 34181, 59928, 65297, 86546

Offset

1,2

Comments

For k>1, numbers such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 61 is prime (see Example section).

a(31) > 2*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 43w61.

Example

5 is in this sequence because (13*10^5 + 83) / 3 = 433361 is prime.
Initial terms and primes associated:
a(1) = 1, 71;
a(2) = 2, 461;
a(3) = 5, 433361;
a(4) = 7, 43333361;
a(5) = 17, 433333333333333361, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(13*10^# + 83) / 3] &]

Prog

(PARI) is(n)=ispseudoprime((13*10^n + 83)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

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

Sequence in context: A193462 A306636 A101150 * A337986 A174281 A301916

Adjacent sequences: A276319 A276320 A276321 * A276323 A276324 A276325

Keyword

nonn,more

Author

Robert Price, Sep 01 2016

Status

approved