login
A212488
Smallest k>0 such that (5^n-k)*5^n-1 and (5^n-k)*5^n+1 are a twin prime pair or 0 if no such k exists.
2
0, 1, 11, 1, 17, 85, 17, 25, 71, 25, 83, 673, 3623, 1069, 401, 1225, 1361, 409, 3449, 2581, 779, 613, 605, 781, 395, 5797, 17, 6967, 755, 361, 3443, 5467, 6857, 679, 53, 9355, 3287, 2941, 22385, 6091, 8423, 685, 13649, 2437, 113, 19393, 19781, 12253, 53603, 21049, 5321, 2149, 21779
OFFSET
1,3
COMMENTS
Conjecture: There is always one such k if n>1.
LINKS
MATHEMATICA
sktp[n_]:=Module[{k=1, c=5^n}, While[AnyTrue[c(c-k)+{1, -1}, CompositeQ], k++]; k]; Join[{0}, Array[ sktp, 60, 2]] (* Harvey P. Dale, Dec 17 2023 *)
PROG
(PFGW64 and SCRIPTIFY)
SCRIPT
DIM nn, 1
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+2
SETS tt, %d, %d\,; nn; kk
PRP (5^nn-kk)*5^nn-1, tt
IF ISPRP THEN GOTO a
IF ISPRIME THEN GOTO a
GOTO loopk
LABEL a
SET jj, jj+1
PRP (5^nn-kk)*5^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: A222803 A377614 A201132 * A373821 A178243 A040131
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jul 18 2012
STATUS
approved