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A214495
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Smallest k>0 such that (3^n-k)*3^n-1 and (3^n-k)*3^n+1 are a twin prime pair.
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6
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1, 1, 11, 19, 7, 1, 23, 31, 53, 49, 47, 139, 49, 101, 97, 399, 87, 281, 37, 329, 893, 497, 203, 883, 213, 1171, 633, 593, 1747, 349, 3843, 479, 2347, 329, 1921, 1299, 2933, 1467, 3097, 1943, 1509, 2077, 2111, 723, 2913, 2307, 963, 361, 297, 1249, 1031, 2153
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OFFSET
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1,3
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COMMENTS
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Conjecture : there is always one such k(n) for each n>0.
Heuristically, as N increases, the average of a(n)/n^2 over n=1 to N tends to 1.2
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LINKS
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MAPLE
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local k;
for k from 1 do
p := (3^n-k)*3^n-1 ;
if isprime(p) and isprime(p+2) then
return k;
end if;
end do:
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MATHEMATICA
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sk[n_]:=Module[{k=1, n3=3^n}, While[!PrimeQ[(n3-k)*n3-1]||!PrimeQ[(n3-k)* n3+1], k++]; k]; Array[sk, 60] (* Harvey P. Dale, Sep 05 2012 *)
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PROG
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(PFGW64 and SCRIPTIFY)
SCRIPT
DIM nn, 0
DIM kk
DIM jj
DIMS tt
OPENFILEOUT myfile, a(n).txt
OPENFILEOUT myf, b(n).txt
LABEL loopn
SET nn, nn+1
SET jj, 0
IF nn>500 THEN END
SET kk, -1
LABEL loopk
SET kk, kk+1
SETS tt, %d, %d\,; nn; kk
PRP (3^nn-kk)*3^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)*3^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
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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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