A201739 Numbers n such that 90*n + 29 is prime.

0, 4, 5, 6, 7, 9, 10, 11, 12, 14, 17, 23, 27, 28, 30, 31, 32, 33, 34, 37, 38, 39, 41, 44, 45, 47, 48, 53, 54, 61, 65, 70, 73, 74, 75, 76, 77, 80, 83, 84, 88, 89, 91, 96, 98, 100, 102, 105, 108, 109, 110, 114, 117, 119, 125, 126, 128, 132, 136, 139, 142, 143

Offset

1,2

Comments

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at the format 90n+29 modulo 9 and modulo 10 we see that all entries of A142327 have digital root 2 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem.)

Links

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

Formula

a(n) = (A142327(n) - 29)/90.

Maple

for n from 0 to 240 do
    p := 90*n+29 ;
    if isprime(p) then
        printf("%d, ", n) ;
    end if;
end do: # R. J. Mathar, Dec 05 2011

Mathematica

Select[Range[0, 400], PrimeQ[90 #+29]&] (* Vincenzo Librandi, Dec 11 2011 *)

Prog

(PARI) forstep(n=29, 1e4, 90, if(isprime(n), print1(n\90", "))) \\ Charles R Greathouse IV, Dec 05 2011
(Magma) [n: n in [0..200] | IsPrime(90*n+29)]; // Vincenzo Librandi, Dec 11 2011

Crossrefs

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

Sequence in context: A068318 A347932 A242337 * A329782 A218044 A066485

Adjacent sequences: A201736 A201737 A201738 * A201740 A201741 A201742

Keyword

nonn,easy

Author

J. W. Helkenberg, Dec 04 2011

Status

approved