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.

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

Lars Blomberg, Table of n, a(n) for n = 1..47

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 *)

Crossrefs

Cf. A000010, A007629, A269307, A269308, A269309, A269311, A269312.

Sequence in context: A123799 A138842 A040462 * A015799 A008604 A110724

Adjacent sequences: A269307 A269308 A269309 * A269311 A269312 A269313

Keyword

nonn,base

Author

Paolo P. Lava, Feb 24 2016

Extensions

a(38) from Lars Blomberg, Jan 18 2018

Status

approved