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A244077 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_(k-j+1)*10^(i-j)}}’, where n’ is the arithmetic derivative of n (see example below). 1

%I

%S 23,29,31,37,53,59,71,73,79,113,131,137,139,173,179,191,193,197,199,

%T 6437,8339,14473,60827,95611,107813

%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_(k-j+1)*10^(i-j)}}’, where n’ is the arithmetic derivative of n (see example below).

%C From 23 to 199 only primes, then composites.

%e If n = 14473, starting from the most significant digit, let us cut the number into the set {1, 14, 144, 1447}. We have:

%e 1’ = 0;

%e 14’ = 9;

%e 144’ = 384;

%e 1447’ = 1.

%e Finally, 0 + 9 + 384 + 1 = 14473’ = 394.

%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 trunc(n/10^k)>0 do c:=trunc(n/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, A244078.

%K nonn,more,base

%O 1,1

%A _Paolo P. Lava_, Jun 19 2014

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Last modified September 17 17:25 EDT 2019. Contains 327136 sequences. (Running on oeis4.)