A201739 - OEIS

%I #19 Sep 08 2022 08:46:01

%S 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,

%T 47,48,53,54,61,65,70,73,74,75,76,77,80,83,84,88,89,91,96,98,100,102,

%U 105,108,109,110,114,117,119,125,126,128,132,136,139,142,143

%N Numbers n such that 90*n + 29 is prime.

%C 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.)

%H Vincenzo Librandi, <a href="/A201739/b201739.txt">Table of n, a(n) for n = 1..10000</a>

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

%p for n from 0 to 240 do

%p     p := 90*n+29 ;

%p     if isprime(p) then

%p         printf("%d,",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Dec 05 2011

%t Select[Range[0,400],PrimeQ[90 #+29]&] (* _Vincenzo Librandi_, Dec 11 2011 *)

%o (PARI) forstep(n=29,1e4,90,if(isprime(n),print1(n\90", "))) \\ _Charles R Greathouse IV_, Dec 05 2011

%o (Magma) [n: n in [0..200] | IsPrime(90*n+29)]; // _Vincenzo Librandi_, Dec 11 2011

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

%K nonn,easy

%O 1,2

%A _J. W. Helkenberg_, Dec 04 2011