%I #22 Sep 03 2024 15:03:17
%S 1,17,85,47,19,71,955,815,223,269,607,1619,2737,53,883,1319,2797,4757,
%T 1585,1535,295,557,3511,269,277,5747,2125,53,13345,2195,109,1175,2995,
%U 5597,3787,1619,6577,8549,3475,5435,4807,20045,23353,9341,2857,2117,1429,16283,25333,7949
%N Smallest k > 0 such that (5^n+k)*5^n-1 and (5^n+k)*5^n+1 are a twin prime pair.
%C Conjecture: there is always one such k for n > 0.
%H Pierre CAMI, <a href="/A212487/b212487.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = A082466(5^n). - _R. J. Mathar_, Jul 20 2012
%p A212487 := proc(n)
%p local k,p ;
%p for k from 1 do
%p p := (5^n+k)*5^n-1 ;
%p if isprime(p) and isprime(p+2) then
%p return k;
%p end if;
%p end do:
%p end proc: # _R. J. Mathar_, Jul 20 2012
%o (PFGW)
%o SCRIPT
%o DIM nn,0
%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. A212488.
%K nonn
%O 1,2
%A _Pierre CAMI_, Jul 18 2012