cp's OEIS Frontend

A007618 a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5.

%I A007618 M3792 #33 Mar 29 2022 08:32:43
%S A007618 5,10,11,13,17,25,32,37,47,58,71,79,95,109,119,130,134,142,149,163,
%T A007618 173,184,197,214,221,226,236,247,260,268,284,298,317,328,341,349,365,
%U A007618 379,398,418,431,439,455,469,488,508,521,529,545,559,578,598,620,628,644
%N A007618 a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5.
%C A007618 a(n) = A004207(n+5) for n > 52. - _Reinhard Zumkeller_, Oct 14 2013
%C A007618 a(2) = 10 and a(590) = 10000 are the first two powers of 10 in this sequence; there are no others below a(19017393928) = 1000000000093. Conjecture: the sequence contains infinitely many powers of 10. - _Charles R Greathouse IV_, Mar 29 2022
%D A007618 N. Agronomof, Problem 4421, L'Intermédiaire des mathématiciens, v. 21 (1914), p. 147. (Mentions sequence starting at 11.) - _N. J. A. Sloane_, Nov 22 2013.
%D A007618 D. R. Kaprekar, Puzzles of the Self-Numbers. 311 Devlali Camp, Devlali, India, 1959.
%D A007618 D. R. Kaprekar, The Mathematics of the New Self Numbers, Privately Printed, 311 Devlali Camp, Devlali, India, 1963.
%D A007618 J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 65.
%D A007618 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007618 Reinhard Zumkeller, <a href="/A007618/b007618.txt">Table of n, a(n) for n = 1..10000</a>
%H A007618 D. R. Kaprekar, <a href="/A003052/a003052_2.pdf">The Mathematics of the New Self Numbers</a> [annotated and scanned]
%H A007618 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F A007618 a(n) = A062028(a(n-1)) for n > 1. - _Reinhard Zumkeller_, Oct 14 2013
%o A007618 (Haskell)
%o A007618 a007618 n = a007618_list !! (n-1)
%o A007618 a007618_list = iterate a062028 5  -- _Reinhard Zumkeller_, Oct 14 2013
%o A007618 (Python)
%o A007618 from itertools import accumulate
%o A007618 def f(an, _): return an + sum(int(d) for d in str(an))
%o A007618 print(list(accumulate([5]*55, f))) # _Michael S. Branicky_, May 10 2021
%Y A007618 Cf. A016052, A006507, A016096.
%K A007618 nonn,base,easy
%O A007618 1,1
%A A007618 _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_