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A269310
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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.
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6
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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
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OFFSET
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1,1
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LINKS
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Lars Blomberg, Table of n, a(n) for n = 1..47
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EXAMPLE
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phi(22) = 10: 2 + 2 = 4; 2 + 4 = 6; 4 + 6 = 10.
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava, Feb 24 2016
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EXTENSIONS
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a(38) from Lars Blomberg, Jan 18 2018
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STATUS
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approved
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