A214495 Smallest k>0 such that (3^n-k)*3^n-1 and (3^n-k)*3^n+1 are a twin prime pair.

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

Offset

1,3

Comments

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

Links

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

Maple

A214495 := proc(n)
    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:
end proc: # R. J. Mathar, Jul 23 2012

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A214496.

Sequence in context: A303237 A066950 A352955 * A162011 A123248 A341899

Adjacent sequences: A214492 A214493 A214494 * A214496 A214497 A214498

Keyword

nonn

Author

Pierre CAMI, Jul 19 2012

Status

approved