A214502 - OEIS

%I #10 Jul 23 2012 19:44:21

%S 1,3,2,5,16,2,2,18,2,8,8,10,14,9,5,43,15,1,56,13,5,151,7,20,107,3,30,

%T 8,16,31,8,21,3,103,57,38,28,37,99,5,15,50,87,31,67,107,1,113,69,12,

%U 41,19,23,43,150,100,49,76,3,159,48,86,49,81,62,48,118,66

%N 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 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.

%H Pierre CAMI, <a href="/A214502/b214502.txt">Table of n, a(n) for n = 1..500</a>

%o PFGW64 and SCRIPTIFY

%o SCRIPT

%o DIM nn, 0

%o DIM kk

%o DIM jj

%o DIMS tt

%o OPENFILEOUT myfile, b(n).txt

%o OPENFILEOUT myf, a(n).txt

%o LABEL loopn

%o SET nn, nn+1

%o SET jj, 0

%o IF nn>500 THEN END

%o SET kk, 0

%o LABEL loopk

%o SET kk, kk+1

%o SETS tt, %d, %d\,; nn; kk

%o PRP (3^nn+kk)*2^nn-1, tt

%o IF ISPRP THEN GOTO a

%o IF ISPRIME THEN GOTO a

%o GOTO loopk

%o LABEL a

%o SET jj, jj+1

%o PRP (3^nn+kk)*2^nn+1, tt

%o IF ISPRP THEN GOTO d

%o IF ISPRIME THEN GOTO d

%o GOTO loopk

%o LABEL d

%o WRITE myfile, tt

%o SETS tt, %d, %d\,; nn; jj

%o WRITE myf, tt

%o GOTO loopn

%Y Cf. A212037, A214497, A214498, A214501.

%K nonn

%O 1,2

%A _Pierre CAMI_, Jul 20 2012