A201816 Numbers k such that 90*k + 13 is prime.

0, 1, 2, 3, 4, 5, 7, 8, 9, 12, 16, 17, 19, 22, 23, 30, 31, 35, 36, 37, 38, 40, 42, 46, 47, 49, 50, 51, 53, 58, 59, 60, 61, 63, 66, 67, 68, 74, 75, 80, 82, 84, 86, 88, 92, 95, 99, 100, 101, 103, 105, 107, 108, 112, 114, 116, 119, 121, 122, 123, 124, 126, 127

Offset: 1

Author

J. W. Helkenberg, Dec 05 2011

Keywords

• nonn
• easy

Comments

Looking at the format 90*k+13 modulo 9 and modulo 10 we see that all entries of A142318 have digital root 4 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804.

Programs

Magma

[n: n in [0..200] | IsPrime(90*n+13)]; // Vincenzo Librandi, Dec 12 2011

Maple

a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, -1, a(n-1))
       while not isprime(90*k+13) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2011

Mathematica

Select[Range[0,4000],PrimeQ[90 #+13]&] (* Vincenzo Librandi, Dec 12 2011 *)

PARI

is(n)=isprime(90*n+13) \\ Charles R Greathouse IV, Jul 12 2016