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%I #14 May 22 2019 14:19:32
%S 14,51,145,285,629,708,807,1318,2362,2548,2869,3789,4087,4811,6031,
%T 6355,10201,15563,17143,17287,17561,19883,20567,21731,22429,23461,
%U 26269,27301,30967,33389,69529,73211,85927,86087,90133,96781,110159,116011,159767,161701,162055,190079
%N Consider a number x. Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach the arithmetic derivative of x.
%H Lars Blomberg, <a href="/A269312/b269312.txt">Table of n, a(n) for n = 1..663</a>
%e 14’ = 9 : 1 + 4 = 5; 4 + 5 = 9.
%e 51’ = 20 : 5 + 1 = 6; 1 + 6 = 7; 6 + 7 = 13; 7 + 13 = 20.
%p with(numtheory): P:=proc(q,h) local a,b,c,k,n,p,t,v; v:=array(1..h);
%p for n from 1 to q do a:=n; b:=ilog10(a)+1; if b>1 then
%p for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);c:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]);
%p while v[t]<c do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p if v[t]=c then print(n); fi; fi; od; end: P(10^9,1000);
%t dn[n_] := If[Abs@n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@n]]]; (* after Michael Somos,Apr 12 2011 *)
%t Select[Range[10^5], # >= 10 && (s = dn[#]; d = IntegerDigits[#]; While[Total[d] < s, d = Join[Rest[d], {Total[d]}]]; Total[d] == s) &] (* _Robert Price_, May 22 2019 *)
%Y Cf. A003415, A007629, A269307, A269308, A269309, A269310, A269311.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Feb 24 2016
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