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A214502 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. 3
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, 8, 16, 31, 8, 21, 3, 103, 57, 38, 28, 37, 99, 5, 15, 50, 87, 31, 67, 107, 1, 113, 69, 12, 41, 19, 23, 43, 150, 100, 49, 76, 3, 159, 48, 86, 49, 81, 62, 48, 118, 66 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A174909 A187943 A301493 * A077039 A269155 A103938
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jul 20 2012
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)