A201822 Numbers k such that 90*k + 77 is prime.

1, 2, 3, 6, 8, 9, 10, 15, 17, 18, 19, 20, 24, 26, 29, 30, 32, 34, 37, 40, 41, 43, 45, 46, 48, 54, 58, 59, 60, 62, 65, 68, 69, 74, 75, 76, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 102, 104, 109, 111, 113, 114, 115, 117, 122, 128, 130, 131, 135, 138, 144

Offset: 1

Author

J. W. Helkenberg, Dec 05 2011

Keywords

• nonn
• easy

Comments

Looking at the format 90k+77 modulo 9 and modulo 10 we see that all entries of A142329 have digital root 5 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

Crossrefs

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820.

Programs

Magma

[n: n in [0..200] | IsPrime(90*n+77)]; // Vincenzo Librandi, Dec 11 2011

Mathematica

Select[Range[0,400],PrimeQ[90 #+77]&] (* Vincenzo Librandi, Dec 11 2011 *)

PARI

is(n)=isprime(90*n+77) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = (A142329(n) - 77)/90.