A007618 a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 5. (Formerly M3792)

5, 10, 11, 13, 17, 25, 32, 37, 47, 58, 71, 79, 95, 109, 119, 130, 134, 142, 149, 163, 173, 184, 197, 214, 221, 226, 236, 247, 260, 268, 284, 298, 317, 328, 341, 349, 365, 379, 398, 418, 431, 439, 455, 469, 488, 508, 521, 529, 545, 559, 578, 598, 620, 628, 644

Offset

1,1

Comments

a(n) = A004207(n+5) for n > 52. - Reinhard Zumkeller, Oct 14 2013

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

References

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. 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).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Index entries for Colombian or self numbers and related sequences

Formula

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

Prog

(Haskell)
a007618 n = a007618_list !! (n-1)
a007618_list = iterate a062028 5  -- Reinhard Zumkeller, Oct 14 2013
(Python)
from itertools import accumulate
def f(an, _): return an + sum(int(d) for d in str(an))
print(list(accumulate([5]*55, f))) # Michael S. Branicky, May 10 2021

Crossrefs

Cf. A016052, A006507, A016096.

Sequence in context: A070791 A173901 A016084 * A004748 A038030 A094016

Adjacent sequences: A007615 A007616 A007617 * A007619 A007620 A007621

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein

Status

approved