A201817 Numbers k such that 90*k + 67 is prime.

0, 1, 3, 6, 8, 9, 10, 13, 14, 17, 19, 20, 23, 29, 30, 31, 33, 35, 36, 42, 44, 47, 50, 51, 56, 57, 61, 62, 63, 64, 66, 69, 70, 72, 73, 76, 77, 79, 83, 85, 90, 94, 96, 98, 100, 101, 103, 107, 108, 110, 117, 118, 120, 121, 122, 125, 127, 128, 129, 133, 138, 139

Offset

1,3

Comments

Looking at the format 90*k + 67 modulo 9 and modulo 10 we see that all entries of A142323 have digital root 4 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.)

Links

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

Maple

a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, -1, a(n-1))
       while not isprime(90*k+67) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2011

Mathematica

Select[Range[0, 4000], PrimeQ[90 #+67]&] (* Vincenzo Librandi, Dec 12 2011 *)

Prog

(Magma) [n: n in [0..200] | IsPrime(90*n+67)]; // Vincenzo Librandi, Dec 12 2011
(PARI) is(n)=isprime(90*n+67) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816.

Sequence in context: A344952 A153307 A265227 * A299240 A004715 A280272

Adjacent sequences: A201814 A201815 A201816 * A201818 A201819 A201820

Keyword

nonn,easy

Author

J. W. Helkenberg, Dec 05 2011

Status

approved