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A004207 a(0) = 1, a(n) = sum of digits of all previous terms.
(Formerly M1115)
56
1, 1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, 91, 101, 103, 107, 115, 122, 127, 137, 148, 161, 169, 185, 199, 218, 229, 242, 250, 257, 271, 281, 292, 305, 313, 320, 325, 335, 346, 359, 376, 392, 406, 416, 427, 440, 448, 464, 478, 497, 517, 530, 538 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

If the leading 1 is omitted, this is the important sequence b(1)=1, for n >= 2, b(n) = b(n-1) + sum of digits of b(n-1). Cf. A016052, A016096, etc. - N. J. A. Sloane, Dec 01 2013

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, Dec 11 2005

More precisely, mod 9 this sequence is 1 (1 2 4 8 7 5)*, the parenthesized part being repeated indefinitely. This shows that this sequence is disjoint from A016052. - N. J. A. Sloane, Oct 15 2013

There are infinitely many even terms (Belov 2003).

a(n) = A007618(n-5) for n > 57; a(n) = A006507(n-4) for n > 15. - Reinhard Zumkeller, Oct 14 2013

REFERENCES

N. Agronomof, Problem 4421, L'Intermédiaire des mathématiciens, v. 21 (1914), p. 147.

D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.

D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately printed, 311 Devlali Camp, Devlali, India, 1963.

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

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

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.

LINKS

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

A. Ya. Belov (ed.), Collection of monster problems in mathematics (in Russian), 2003. Problem 39.

D. R. Kaprekar, The Mathematics of the New Self Numbers [annotated and scanned]

Project Euler, Problem 551: Sum of digits sequence.

Kenneth B. Stolarsky, The sum of a digitaddition series, Proc. Amer. Math. Soc. 59 (1976), no. 1, 1--5. MR0409340 (53 #13099)

Index entries for Colombian or self numbers and related sequences

FORMULA

For n>1, a(n) = a(n-1) + sum of digits of a(n-1).

For n > 1: a(n) = A062028(a(n-1)). - Reinhard Zumkeller, Oct 14 2013

MAPLE

read("transforms") :

A004207 := proc(n)

    option remember;

    if n = 0 then

        1;

    else

        add( digsum(procname(i)), i=0..n-1) ;

    end if;

end proc: # R. J. Mathar, Apr 02 2014

MATHEMATICA

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

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

PROG

(Haskell)

a004207 n = a004207_list !! n

a004207_list = 1 : iterate a062028 1

-- Reinhard Zumkeller, Oct 14 2013, Sep 12 2011

(PARI)

a(n) = { my(f(d, i) = d+vecsum(digits(d)), S=vector(n)); S[1]=1; for(k=1, n-1, S[k+1] = fold(f, S[1..k])); S } \\ Satish Bysany, Mar 03 2017

CROSSREFS

Cf. A016052, A016096, A033298, A007612, A007953, A229527, A230107.

For the base-2 analog see A010062.

A065075 gives sum of digits of a(n).

See A219675 for an essentially identical sequence.

Sequence in context: A130917 A007612 A112395 * A219675 A062729 A004620

Adjacent sequences:  A004204 A004205 A004206 * A004208 A004209 A004210

KEYWORD

nonn,base,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

Typo in definition fixed by Reinhard Zumkeller, Sep 14 2011

STATUS

approved

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Last modified July 26 18:35 EDT 2017. Contains 289839 sequences.