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.

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, 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, 29, 48, 100, 72, 31, 128, 27, 33, 29, 41, 14, 21, 40, 19, 52, 36, 79, 54

Offset

1,2

Comments

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.

Heuristically, the average of a(n)/n over n=1 to N tends to 0.61 as N increases.

Links

Pierre CAMI, Table of n, a(n) for n = 1..500

Prog

PFGW64 and SCRIPTIFY
SCRIPT
DIM nn, 0
DIM kk
DIM jj
DIMS tt
OPENFILEOUT myfile, b(n).txt
OPENFILEOUT myf, a(n).txt
LABEL loopn
SET nn, nn+1
SET jj, 0
IF nn>500 THEN END
SET kk, 0
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP (3^nn-kk)*2^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
SET jj, jj+1
PRP (3^nn-kk)*2^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
WRITE myfile, tt
SETS tt, %d, %d\,; nn; jj
WRITE myf, tt
GOTO loopn

Crossrefs

Cf. A212037, A214497, A214498, A214502.

Sequence in context: A374832 A053734 A238904 * A318665 A057856 A117939

Adjacent sequences: A214498 A214499 A214500 * A214502 A214503 A214504

Keyword

nonn

Author

Pierre CAMI, Jul 20 2012

Status

approved