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A212487 Smallest k > 0 such that (5^n+k)*5^n-1 and (5^n+k)*5^n+1 are a twin prime pair.

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