A016096 a(n+1) = a(n) + sum of its digits, with a(1) = 9.

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 117, 126, 135, 144, 153, 162, 171, 180, 189, 207, 216, 225, 234, 243, 252, 261, 270, 279, 297, 315, 324, 333, 342, 351, 360, 369, 387, 405, 414, 423, 432, 441, 450, 459, 477, 495, 513, 522, 531, 540

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn
• base

References

• 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.

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

Crossrefs

Cf. A004207, A016052, A007618, A006507.

Programs

Haskell

a016096 n = a016096_list !! (n-1)
a016096_list = iterate a062028 9  -- Reinhard Zumkeller, Oct 14 2013

Python

from itertools import islice
def A016096_gen(): # generator of terms
    a = 9
    while True:
        yield a
        a += sum(int(d) for d in str(a))
A016096_list = list(islice(A016096_gen(),20)) # Chai Wah Wu, Mar 29 2022

Formula

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