A201820 Numbers k such that 90*k + 23 is prime.

0, 1, 3, 4, 6, 7, 8, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 28, 29, 32, 34, 39, 40, 42, 45, 47, 50, 52, 53, 55, 57, 59, 63, 64, 67, 68, 70, 76, 78, 84, 85, 87, 90, 95, 96, 97, 99, 102, 103, 105, 108, 109, 110, 112, 113, 116, 119, 122, 123, 125, 129, 131

Offset: 1

Author

J. W. Helkenberg, Dec 05 2011

Keywords

• nonn
• easy

Comments

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at the format 90*k+23 modulo 9 and modulo 10 we see that all entries of A142324 have digital root 5 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, A201816, A201817, A201818.

Programs

Magma

[n: n in [0..200] | IsPrime(90*n+23)]; // Vincenzo Librandi, Dec 11 2011

Mathematica

Select[Range[0,400],PrimeQ[90 #+23]&] (* Vincenzo Librandi, Dec 11 2011 *)

PARI

is(n)=isprime(90*n+23) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = (A142324(n) - 23)/90.