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A269310 Consider a number x > 1. 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 Euler totient function of x.

%I A269310 #31 May 21 2019 23:55:19
%S A269310 22,44,55,88,98,136,162,166,241,462,1020,2040,2416,2899,3060,4080,
%T A269310 5110,7942,10738,10996,15006,24822,57040,67054,70625,75588,96888,
%U A269310 261524,301834,507471,735840,816584,2893877,6081064,8155616,16513570,18772258,40833543
%N A269310 Consider a number x > 1. 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 Euler totient function of x.
%H A269310 Lars Blomberg, <a href="/A269310/b269310.txt">Table of n, a(n) for n = 1..47</a>
%e A269310 phi(22) = 10: 2 + 2 = 4; 2 + 4 = 6; 4 + 6 = 10.
%p A269310 with(numtheory): P:=proc(q,h) local a,b,k,n,t,v; v:=array(1..h);
%p A269310 for n from 2 to q do a:=n; b:=ilog10(a)+1; if b>1 then
%p A269310 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);
%p A269310 while v[t]<phi(n) do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
%p A269310 if v[t]=phi(n) then print(n); fi; fi; od; end: P(10^6, 1000);
%t A269310 Select[Range[2,10^5], (t = EulerPhi[#]; d = IntegerDigits[#]; While[Total[d] < t, d = Join[Rest[d], {Total[d]}]]; Total[d] == t) &] (* _Robert Price_, May 17 2019 *)
%Y A269310 Cf. A000010, A007629, A269307, A269308, A269309, A269311, A269312.
%K A269310 nonn,base
%O A269310 1,1
%A A269310 _Paolo P. Lava_, Feb 24 2016
%E A269310 a(38) from _Lars Blomberg_, Jan 18 2018