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A213884 For the smallest k >= 1, the smallest single-digit j such that (10^k-j)*10^n-1 is prime.

%I A213884 #25 Jan 16 2025 11:52:56
%S A213884 1,4,1,2,2,5,1,2,1,2,1,4,4,5,5,1,4,7,1,4,2,4,4,1,2,8,7,4,1,1,2,1,1,4,
%T A213884 7,4,1,1,7,4,8,2,7,4,8,8,7,2,2,1,8,2,8,5,7,1,8,4,8,1,4,1,4,7,1,2,8,2,
%U A213884 4,1,4,8,4,5,8,2,1,2,7,7,5,1,4,8,7,4,1,4,2,2,4,5
%N A213884 For the smallest k >= 1, the smallest single-digit j such that (10^k-j)*10^n-1 is prime.
%C A213884 These j are the associated shifts to be paired with the k-values of A213883. There are no multiples of 3 here, as explained in A213883.
%C A213884 For the first 2200 values of n, there is always at least one pair (k,j) that delivers a prime with the conditions.
%H A213884 Pierre CAMI, <a href="/A213884/b213884.txt">Table of n, a(n) for n = 1..2200</a>
%e A213884 j=1 associated with the prime 89, j=4 associated with 599, j=1 associated with 8999, j=2 with 79999 are the first 4 entries.
%p A213884 A213884 := proc(n)
%p A213884     for k from 1 do
%p A213884         for j from 0 to 9 do
%p A213884             if isprime( (10^k-j)*10^n-1) then
%p A213884                 return j;
%p A213884             end if;
%p A213884         end do:
%p A213884     end do:
%p A213884     return 0 ;
%p A213884 end proc: # _R. J. Mathar_, Jul 20 2012
%o A213884 (PFGW & SCRIPT)
%o A213884 SCRIPT
%o A213884 DIM nn, 0
%o A213884 DIM jj
%o A213884 DIM kk
%o A213884 DIMS tt
%o A213884 OPENFILEOUT myfile, a(n).txt
%o A213884 LABEL loopn
%o A213884 SET nn, nn+1
%o A213884 IF nn>2200 THEN END
%o A213884 SET kk, 0
%o A213884 LABEL loopk
%o A213884 SET kk, kk+1
%o A213884 IF kk>2*nn THEN GOTO loopn
%o A213884 SET jj, 0
%o A213884 LABEL loopj
%o A213884 SET jj, jj+1
%o A213884 IF jj%3==0 THEN SET jj, jj+1
%o A213884 IF jj>9 THEN GOTO loopk
%o A213884 SETS tt, %d, %d, %d\,; nn; kk; jj
%o A213884 PRP (10^kk-jj)*10^nn-1, tt
%o A213884 IF ISPRP THEN GOTO a
%o A213884 IF ISPRIME THEN GOTO a
%o A213884 GOTO loopj
%o A213884 LABEL a
%o A213884 WRITE myfile, tt
%o A213884 GOTO loopn
%Y A213884 Cf. A213883.
%K A213884 nonn
%O A213884 1,2
%A A213884 _Pierre CAMI_, Jun 29 2012