cp's OEIS Frontend

A214501 The size of the set of numbers k>=0 such that all (3^n-k)*2^n-1 are prime but only the last (largest) (3^n-k)*2^n+1 is also an associated twin prime.

%I A214501 #8 Jul 23 2012 19:43:32
%S A214501 1,2,1,1,2,1,1,6,1,2,1,6,8,8,41,11,5,8,11,24,35,15,22,5,11,19,15,16,
%T A214501 60,10,21,35,82,13,8,4,1,44,4,33,12,29,59,45,17,60,4,1,119,38,6,35,1,
%U A214501 29,48,100,72,31,128,27,33,29,41,14,21,40,19,52,36,79,54
%N A214501 The size of the set of numbers k>=0 such that all (3^n-k)*2^n-1 are prime but only the last (largest) (3^n-k)*2^n+1 is also an associated twin prime.
%C A214501 Starting at a count of zero, we consider for increasing k>=0 the pairs (3^n-k)*2^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime.
%C A214501 Heuristically, the average of a(n)/n over n=1 to N tends to 0.61 as N increases.
%H A214501 Pierre CAMI, <a href="/A214501/b214501.txt">Table of n, a(n) for n = 1..500</a>
%o A214501 PFGW64 and SCRIPTIFY
%o A214501 SCRIPT
%o A214501 DIM nn, 0
%o A214501 DIM kk
%o A214501 DIM jj
%o A214501 DIMS tt
%o A214501 OPENFILEOUT myfile, b(n).txt
%o A214501 OPENFILEOUT myf, a(n).txt
%o A214501 LABEL loopn
%o A214501 SET nn, nn+1
%o A214501 SET jj, 0
%o A214501 IF nn>500 THEN END
%o A214501 SET kk, 0
%o A214501 LABEL loopk
%o A214501 SET kk, kk+1
%o A214501 SETS tt, %d, %d\,; nn; kk
%o A214501 PRP (3^nn-kk)*2^nn-1, tt
%o A214501 IF ISPRP THEN GOTO a
%o A214501 IF ISPRIME THEN GOTO a
%o A214501 GOTO loopk
%o A214501 LABEL a
%o A214501 SET jj, jj+1
%o A214501 PRP (3^nn-kk)*2^nn+1, tt
%o A214501 IF ISPRP THEN GOTO d
%o A214501 IF ISPRIME THEN GOTO d
%o A214501 GOTO loopk
%o A214501 LABEL d
%o A214501 WRITE myfile, tt
%o A214501 SETS tt, %d, %d\,; nn; jj
%o A214501 WRITE myf, tt
%o A214501 GOTO loopn
%Y A214501 Cf. A212037, A214497, A214498, A214502.
%K A214501 nonn
%O A214501 1,2
%A A214501 _Pierre CAMI_, Jul 20 2012