A016052 a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digits.

3, 6, 12, 15, 21, 24, 30, 33, 39, 51, 57, 69, 84, 96, 111, 114, 120, 123, 129, 141, 147, 159, 174, 186, 201, 204, 210, 213, 219, 231, 237, 249, 264, 276, 291, 303, 309, 321, 327, 339, 354, 366, 381, 393, 408, 420, 426, 438, 453, 465, 480, 492

Offset

1,1

Comments

Mod 9 this sequence is 3, 6, 3, 6, 3, 6, ... This shows that this sequence is disjoint from A004207. - N. J. A. Sloane, Oct 15 2013

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.

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

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

a(n) - a(n-1) = A084228(n+1). - Robert G. Wilson v, Jun 27 2014

Mathematica

NestList[# + Total[IntegerDigits[#]] &, 3, 51] (* Jayanta Basu, Aug 11 2013 *)
a[1] = 3; a[n_] := a[n] = a[n - 1] + Total@ IntegerDigits@ a[n - 1]; Array[a, 80] (* Robert G. Wilson v, Jun 27 2014 *)

Prog

(Haskell)
a016052 n = a016052_list !! (n-1)
a016052_list = iterate a062028 3  -- Reinhard Zumkeller, Oct 14 2013
(PARI)
a_list(nn) = { my(f(n, i) = n + vecsum(digits(n)), S=vector(nn+1)); S[1]=3; for(k=2, #S, S[k] = fold(f, S[1..k-1])); S[2..#S] } \\ Satish Bysany, Mar 04 2017
(Python)
from itertools import islice
def A016052_gen(): # generator of terms
    yield (a:=3)
    while True: yield (a:=a+sum(map(int, str(a))))
A016052_list = list(islice(A016052_gen(), 20)) # Chai Wah Wu, Jun 16 2024

Crossrefs

Cf. A004207, A007618, A006507, A016096, A230107, A230286, A230287, A084228.

Sequence in context: A016051 A070790 A114614 * A323649 A115803 A290258

Adjacent sequences: A016049 A016050 A016051 * A016053 A016054 A016055

Keyword

nonn,base,easy

Author

Robert G. Wilson v

Status

approved