0,3

If the initial 1 is dropped, we get the sequence defined by a(1) = 1, a(n) = a(n-1) + sum of digits of a(n-1).

Same digital roots as A065075 (Sum of digits of the sum of the preceding numbers) and A001370 (Sum of digits of 2^n)); they end in the cycle {1 2 4 8 7 5}. - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 11 2005

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 65.

G. E. Stevens and L. G. Hunsberger, A Result and a Conjecture on Digit Sum Sequences, J. Recreational Math. 27, no. 4 (1995), pp. 285-288.

T. D. Noe, Table of n, a(n) for n=0..10000

a[1]:=1:a[2]:=1:for n from 3 to 100 do d:=a[n-1]:s:=0:while d>0 do c:=d mod 10:s:=s+c:d:=(d-c)/10 od:e:=a[n-2]:t:=0:while e>0 do c:=e mod 10:t:=t+c:e:=(e-c)/10 od:a[n]:=a[n-1]+s od: seq(a[n], n=1..54); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2009]

f[s_] := Append[s, Plus @@ Flatten[IntegerDigits /@ s]]; Nest[f, {1}, 55] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006)

f[n_] := n + Plus @@ IntegerDigits@n; Join[{1}, NestList[f, 1, 80]] (Alonso Del Arte, May 27 2006)

Cf. A016052, A033298, A007612.

Sequence in context: A130917 A007612 A112395 this_sequence A062729 A004620 A018618

Adjacent sequences: A004204 A004205 A004206 this_sequence A004208 A004209 A004210

nonn,base,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

Errors from 25th term on corrected by Leonid Broukhis Mar 15 1996.