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%I #10 Jul 20 2012 11:28:51
%S 1,0,3,1,3,2,2,2,5,1,2,2,0,4,1,2,2,2,5,0,7,2,2,3,2,4,0,2,3,2,2,5,2,2,
%T 4,0,2,3,0,2,0,1,4,1,3,1,4,2,1,4,5,1,4,2,0,1,4,3,3,3,5,1,1,3,1,3,1,2,
%U 5,4,2,1,2,3,1,4,2,2,1,1,5,2,2,2,0,2,2,1,3,4,3,5,4,1,1,2,3,2,4,1
%N Number of prime numbers of the form (10^k-1)*10^n-1 with 0<k<=2*n
%C The condition k<=2*n sets a limit of the numbers to be checked for primeness.
%C The sequence counts a subset of the primes considered in A213886.
%C Statistics over n=1 to 1000: 105 values of a(n) are zero, the average value of a(n) is 2.33.
%H Pierre CAMI, <a href="/A213885/b213885.txt">Table of n, a(n) for n = 1..1000</a>
%e (10^1-1)*10-1=89 prime
%e (10^2-1)*10^1-1=989 composite so a(1)=1
%e (10^1-1)*10^2-1=899 composite
%e (10^2-1)*10^2-1=9899 composite
%e (10^3-1)*10^2-1=99899 composite
%e (10^4-1)*10^2-1=999899 composite so a(2)=0
%p A213885 := proc(n)
%p local a,k;
%p a := 0 ;
%p for k from 1 to 2*n do
%p if isprime((10^k-1)*10^n-1) then
%p a := a+1 ;
%p end if;
%p end do:
%p return a;
%p end proc: # _R. J. Mathar_, Jul 19 2012
%o (PFGW64 and SCRIPTIFY)
%o SCRIPT
%o DIM nn,0
%o DIM kk
%o DIMS tt
%o OPENFILEOUT myfile,a(n).txt
%o LABEL loopn
%o SET nn,nn+1
%o IF nn>1000 THEN END
%o SET kk,0
%o LABEL loopk
%o SET kk,kk+1
%o IF kk>2*nn THEN GOTO loopn
%o SETS tt,%d,%d\,;nn;kk
%o PRP (10^kk-1)*10^nn-1,tt
%o IF ISPRP THEN GOTO a
%o IF ISPRIME THEN GOTO a
%o GOTO loopk
%o LABEL a
%o WRITE myfile,tt
%o GOTO loopk
%K nonn
%O 1,3
%A _Pierre CAMI_, Jul 10 2012
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