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%I #24 Jul 20 2012 15:22:14
%S 1,1,1,1,1,1,1,1,2,1,3,2,1,1,3,5,5,3,1,3,3,1,1,9,1,1,1,1,1,7,3,6,4,1,
%T 4,4,1,15,10,1,7,3,1,3,2,2,4,6,1,3,5,20,1,1,1,8,10,7,15,10,1,4,2,5,8,
%U 3,23,11,2,2,9,3,1,5,4,1,6,3,18,2
%N Least number k such that (10^k-j)*10^n-1 is prime for some single-digit j or 0 if no such prime with 1<=k, 0<=j<=9 exists.
%C j cannot be 0, 3, 6 or 9 because we are searching for repdigit primes with k-1 times the digit 9, one digit (9-j), and n least-significant digits 9 (so n+k-1 times the digit 9 in total). If j is a multiple of 3, that number is also a multiple of 3 and not prime.
%C Conjecture: there is always at least one (k,j) solution for each n.
%H Pierre CAMI, <a href="/A213883/b213883.txt">Table of n, a(n) for n = 1..2200</a>
%e Refers to the primes 89, 599, 8999, 79999, 799999, 4999999, 89999999,...
%p A213883 := proc(n)
%p for k from 1 to 2*n-1 do
%p for j from 0 to 9 do
%p if isprime( (10^k-j)*10^n-1) then
%p return k;
%p end if;
%p end do:
%p end do:
%p return 0 ;
%p end proc: # _R. J. Mathar_, Jul 20 2012
%o SCRIPT
%o DIM nn,0
%o DIM jj
%o DIM kk
%o DIMS tt
%o OPENFILEOUT myfile,a(n).txt
%o LABEL loopn
%o SET nn,nn+1
%o IF nn>2200 THEN END
%o SET kk,0
%o LABEL loopk
%o SET kk,kk+1
%o IF kk>2*nn THEN GOTO loopn
%o SET jj,0
%o LABEL loopj
%o SET jj,jj+1
%o IF jj%3==0 THEN SET jj,jj+1
%o IF jj>9 THEN GOTO loopk
%o SETS tt,%d,%d,%d\,;nn;kk;jj
%o PRP (10^kk-jj)*10^nn-1,tt
%o IF ISPRP THEN GOTO a
%o IF ISPRIME THEN GOTO a
%o GOTO loopj
%o LABEL a
%o WRITE myfile,tt
%o GOTO loopn
%Y Cf. A213790, A213884 (corresponding j).
%K nonn
%O 1,9
%A _Pierre CAMI_, Jun 26 2012
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