A212488 - OEIS

%I #15 Dec 17 2023 13:45:41

%S 0,1,11,1,17,85,17,25,71,25,83,673,3623,1069,401,1225,1361,409,3449,

%T 2581,779,613,605,781,395,5797,17,6967,755,361,3443,5467,6857,679,53,

%U 9355,3287,2941,22385,6091,8423,685,13649,2437,113,19393,19781,12253,53603,21049,5321,2149,21779

%N 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.

%C Conjecture: There is always one such k if n>1.

%H Pierre CAMI, <a href="/A212488/b212488.txt">Table of n, a(n) for n = 1..501</a>

%t 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 *)

%o (PFGW64 and SCRIPTIFY)

%o SCRIPT

%o DIM nn, 1

%o DIM kk

%o DIM jj

%o DIMS tt

%o OPENFILEOUT myfile, a(n).txt

%o OPENFILEOUT myf, b(n).txt

%o LABEL loopn

%o SET nn, nn+1

%o SET jj, 0

%o IF nn>500 THEN END

%o SET kk, -1

%o LABEL loopk

%o SET kk, kk+2

%o SETS tt, %d, %d\,; nn; kk

%o PRP (5^nn-kk)*5^nn-1, tt

%o IF ISPRP THEN GOTO a

%o IF ISPRIME THEN GOTO a

%o GOTO loopk

%o LABEL a

%o SET jj, jj+1

%o PRP (5^nn-kk)*5^nn+1, tt

%o IF ISPRP THEN GOTO d

%o IF ISPRIME THEN GOTO d

%o GOTO loopk

%o LABEL d

%o WRITE myfile, tt

%o SETS tt, %d, %d\,; nn; jj

%o WRITE myf, tt

%o GOTO loopn

%Y Cf. A212487

%K nonn

%O 1,3

%A _Pierre CAMI_, Jul 18 2012