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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.
6
22, 44, 55, 88, 98, 136, 162, 166, 241, 462, 1020, 2040, 2416, 2899, 3060, 4080, 5110, 7942, 10738, 10996, 15006, 24822, 57040, 67054, 70625, 75588, 96888, 261524, 301834, 507471, 735840, 816584, 2893877, 6081064, 8155616, 16513570, 18772258, 40833543
OFFSET
1,1
LINKS
EXAMPLE
phi(22) = 10: 2 + 2 = 4; 2 + 4 = 6; 4 + 6 = 10.
MAPLE
with(numtheory): P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
for n from 2 to q do a:=n; b:=ilog10(a)+1; if b>1 then
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);
while v[t]<phi(n) do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=phi(n) then print(n); fi; fi; od; end: P(10^6, 1000);
MATHEMATICA
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 *)
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 24 2016
EXTENSIONS
a(38) from Lars Blomberg, Jan 18 2018
STATUS
approved