Search: id:A004207
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%I A004207 M1115
%S A004207 1,1,2,4,8,16,23,28,38,49,62,70,77,91,101,103,107,115,122,127,137,148,
%T A004207 161,169,185,199,218,229,242,250,257,271,281,292,305,313,320,325,
%U A004207 335,346,359,376,392,406,416,427,440,448,464,478,497,517,530,538
%N A004207 a(1) = 1, a(n) = sum of digits of all previous terms.
%C A004207 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).
%C A004207 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
%D A004207 J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 65.
%D A004207 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004207 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.
%H A004207 T. D. Noe, <a href="b004207.txt">Table of n, a(n) for n=0..10000</a>
%p A004207 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]
%t A004207 f[s_] := Append[s, Plus @@ Flatten[IntegerDigits /@ s]]; Nest[f, {1}, 
               55] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 26 2006)
%t A004207 f[n_] := n + Plus @@ IntegerDigits@n; Join[{1}, NestList[f, 1, 80]] (Alonso 
               Del Arte, May 27 2006)
%Y A004207 Cf. A016052, A033298, A007612.
%Y A004207 Sequence in context: A130917 A007612 A112395 this_sequence A062729 A004620 
               A018618
%Y A004207 Adjacent sequences: A004204 A004205 A004206 this_sequence A004208 A004209 
               A004210
%K A004207 nonn,base,easy,nice
%O A004207 0,3
%A A004207 N. J. A. Sloane (njas(AT)research.att.com).
%E A004207 Errors from 25th term on corrected by Leonid Broukhis Mar 15 1996.

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