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%I #10 Jun 24 2014 05:47:42
%S 13,17,23,37,43,53,67,73,83,97,131,211,241,271,311,331,431,461,541,
%T 571,631,641,661,761,811,911,941,971,1601,3701,5101,5701,6101,6701,
%U 8101,9601,13001,16138,18497,19001,22879,24001,54001,69001,93001,97001,99361,270001
%N Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that n’ = Sum_{i=1..k-1}{Sum_{j=1..i}{d_(j)*10^(j-1)}}’, where n’ is the arithmetic derivative of n (see example below).
%C Mainly primes.
%e If n = 16138, starting from the least significant digit, let us cut the number into the set {8, 38, 138, 6138}. We have:
%e 8’ = 12;
%e 38’ = 21;
%e 138’ = 121;
%e 6138’ = 7917.
%e Finally, 12 + 21 + 121 + 7917 = 16138’ = 8071.
%p with(numtheory); P:=proc(q) local a,c,k,n,p;
%p for n from 10 to q do
%p a:=0; k:=1; while (n mod 10^k)<n do c:=(n mod 10^k);
%p a:=a+c*add(op(2,p)/op(1,p),p=ifactors(c)[2]); k:=k+1; od;
%p if a=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]) then print(n);
%p fi; od; end: P(10^10);
%Y Cf. A003415, A240894-A240903, A241207, A241502, A241503, A244068, A244069, A244077.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Jun 19 2014
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