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A205321
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Smallest k>=0 such that (2^n+k)*2^n-1 and (2^n+k)*2^n+1 are a twin prime pair.
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3
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0, 11, 1, 11, 4, 11, 13, 116, 34, 14, 241, 44, 97, 458, 337, 59, 604, 206, 67, 167, 424, 179, 97, 326, 259, 284, 1177, 77, 328, 356, 508, 74, 1798, 749, 2197, 1289, 643, 839, 1171, 1427, 814, 2564, 31, 4244, 379, 5099, 3706, 4871, 2719, 3194, 7057, 122, 5329, 2636, 301, 2852, 3793
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OFFSET
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1,2
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COMMENTS
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Conjecture : there is at least one k for each n.
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LINKS
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FORMULA
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MAPLE
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local a, p ;
for a from 0 do
p := (2^n+a)*2^n-1 ;
if isprime(p) and isprime(p+2) then
return a;
end if;
end do:
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PROG
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(PFGW64 and SCRIPTIFY)
SCRIPT
DIM nn, 0
DIM kk
DIMS tt
OPENFILEOUT myfile, a(n).txt
LABEL loopn
SET nn, nn+1
IF nn>825 THEN END
SET kk, -1
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP (2^nn+kk)*2^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
PRP (2^nn+kk)*2^nn+1, tt
IF ISPRP THEN GOTO d
IF ISPRIME THEN GOTO d
GOTO loopk
LABEL d
WRITE myfile, tt
GOTO loopn
Results in a(n).txt file
all kk values such that (2^nn+kk)*2^nn-1 is prime in pfgw-primes.log and pfgw.log files
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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