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Numbers n such that 90n + 73 is prime.
21

%I #26 May 02 2017 18:59:13

%S 0,1,4,5,6,9,11,12,15,18,19,20,22,23,27,28,29,32,36,39,40,42,43,49,51,

%T 54,55,56,61,62,63,65,70,72,74,75,85,88,91,92,93,95,96,97,98,103,104,

%U 106,109,110,113,114,116,127,128,131

%N Numbers n such that 90n + 73 is prime.

%C This sequence results from the propagation (addition) of 12 Fibonacci-like sequences; this sequence contains (recovers) all digital root 1 and last digit 3 prime numbers.

%H Ivan Neretin, <a href="/A195993/b195993.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A142326(n)-73)/90.

%p A142326 := proc(n)

%p option remember;

%p if n = 1 then

%p 73 ;

%p else

%p a := nextprime(procname(n-1)) ;

%p while (a mod 45) <> 28 do

%p a := nextprime(a) ;

%p end do;

%p return a;

%p end if;

%p end proc:

%p A195993 := proc(n)

%p (A142326(n)-73)/90 ;

%p end proc:

%p seq(A195993(n),n=1..80) ; # _R. J. Mathar_, Oct 31 2011

%t Select[Range[0,200],PrimeQ[90#+73]&] (* _Harvey P. Dale_, May 05 2014 *)

%o (PARI) is(n)=isprime(90*n+73) \\ _Charles R Greathouse IV_, Apr 25 2016

%Y Cf. A181732, A198382.

%K nonn,easy

%O 1,3

%A _J. W. Helkenberg_, Oct 27 2011