

A212038


The size of the set of numbers k>=0 such that all (2^nk)*2^n1 are prime but only (2^nk)*2^n+1 with the largest k is also the associated twin prime.


1



1, 7, 5, 2, 4, 11, 6, 1, 3, 2, 31, 2, 11, 11, 11, 6, 30, 16, 2, 36, 90, 56, 11, 52, 13, 36, 10, 62, 20, 31, 23, 28, 30, 14, 47, 22, 10, 5, 104, 39, 11, 14, 64, 184, 209, 176, 193, 162, 25, 38, 23, 5, 27, 157, 5, 17, 32, 90, 1, 199, 96, 83, 29, 82, 12, 220, 19, 40, 37, 13, 16, 120, 11, 130, 12, 77, 202
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OFFSET

4,2


COMMENTS

Search set similar to A212037 but the sign of k in the prime form is switched.
Heuristically the average of a(n)/n for n=1 to N tends to 1 as N increases.


LINKS

Pierre CAMI, Table of n, a(n) for n = 4..825


MAPLE

A212038 := proc(n)
local a, k, p ;
a := 0 ;
for k from 0 do
p := (2^nk)*2^n1 ;
if isprime(p) then
a := a+1 ;
end if;
if isprime(p) and isprime(p+2) then
return a;
end if;
end do:
end proc: # R. J. Mathar, Jul 21 2012


PROG

SCRIPT
DIM nn, 3
DIM jj
DIM kk
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
IF nn>825 THEN END
SET kk, 1
SET jj, 0
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP (2^nnkk)*2^nn1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
SET jj, jj+1
PRP (2^nnkk)*2^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
SETS tt, %d, %d\,; nn; jj
WRITE myfile, tt
GOTO loopn


CROSSREFS

Cf. A191619, A191620, A205322.
Sequence in context: A070404 A258370 A135537 * A335863 A112545 A021934
Adjacent sequences: A212035 A212036 A212037 * A212039 A212040 A212041


KEYWORD

nonn


AUTHOR

Pierre CAMI, Jul 14 2012


STATUS

approved



