A269309 Consider the Euler totient function of 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 x.

13, 21, 63, 177, 206, 412, 655, 824, 1990, 2637, 11438, 12485, 23846, 34132, 40528, 56202, 87539, 94597, 1288999, 3075239, 3106991, 20689503, 31173397, 46230492, 65889985, 79476719, 170859904, 266368503, 295845211, 420471958, 445169688, 797687940, 962257660

Offset: 1

Author

Paolo P. Lava, Feb 24 2016

Keywords

• nonn
• base

Examples

			phi(13) = 12 : 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8; 5 + 8 = 13.
		

Crossrefs

Cf. A000010, A007629, A269307, A269308, A269310, A269311, A269312.

Programs

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:=phi(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]
				

Mathematica

Select[Range[10^5], EulerPhi[#] >= 10 && (d = IntegerDigits[EulerPhi[#]]; While[Total[d] < #, d = Join[Rest[d], {Total[d]}];]; Total[d] == #) &] (* Robert Price, May 21 2019 *)

Extensions

a(19)-a(33) from Lars Blomberg, Jan 18 2018