A084228 -id:A084228 - cp's OEIS frontend

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

Robert G. Wilson v

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

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.
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 34-35.

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

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

a016052 n = a016052_list !! (n-1)
a016052_list = iterate a062028 3  -- Reinhard Zumkeller, Oct 14 2013

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 *)

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

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

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

A230287 First differences of A016052/3 (= A230286).

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 1, 2, 4, 2, 4, 5, 4, 5, 1, 2, 1, 2, 4, 2, 4, 5, 4, 5, 1, 2, 1, 2, 4, 2, 4, 5, 4, 5, 4, 2, 4, 2, 4, 5, 4, 5, 4, 5, 4, 2, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 7, 5, 4, 5, 4, 5, 7, 8, 4, 5, 4, 5, 7, 8, 4, 5, 7, 5, 7, 5, 4, 5, 7, 8, 7, 2, 1, 2, 4, 2, 4, 5, 4, 5, 1, 2, 1, 2, 4, 2, 4, 5, 4, 5, 4

Offset: 1

Reinhard Zumkeller and N. J. A. Sloane, Oct 16 2013

This sequence captures the essence of A016052.

Essentially the same as A084228/3.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for Colombian or self numbers and related sequences

Cf. A004207, A016052, A230286, A084228, A065075.

a230287 n = a230287_list !! (n-1)
a230287_list = zipWith (-) (tail a230286_list) a230286_list

A084229 Let b(1)=1, b(2)=2, b(n) = sum of digits of b(1)+b(2)+b(3)+...+b(n-1), sequence gives values of n such that b(n)=3.

Original entry on oeis.org

3, 5, 7, 9, 17, 19, 27, 29, 87, 95, 97, 159, 591, 599, 601, 663, 1143, 4609, 4617, 4619, 4681, 5161, 8993, 13165, 38277, 38279, 38341, 38821, 42653, 46825, 75043, 79223, 327015, 327023, 327025, 327087, 327567, 331399, 335571, 363789, 367969, 642981, 647153, 2847029, 2847031, 2847093, 2847573

Offset: 1

Benoit Cloitre, Jun 21 2003

The {b(n)} sequence is A084228. - N. J. A. Sloane, Jun 26 2014

Note that b(k)==0 (mod 3) for n>2.

Robert G. Wilson v, Table of n, a(n) for n = 1..107

Cf. A065075, A084228.

k = 3; lst = {}; a = 3; While[k < 100000001, b = a + Total@ IntegerDigits@ a; If[b == a + 3, AppendTo[lst, k]; Print@ k]; a = b; k++]; lst (* Robert G. Wilson v, Jun 27 2014 *)

upto(n)={my(L=List(), s=3, k=3); while(k<=n, my(t=sumdigits(s)); if(t==3, listput(L,k)); s+=t; k++); Vec(L)} \\ Andrew Howroyd, Oct 16 2024

Conjecture : a(n)/n^3 is bounded.

a(23) onward from Robert G. Wilson v, Jun 27 2014

cp's OEIS Frontend

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

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A230287 First differences of A016052/3 (= A230286).

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A084229 Let b(1)=1, b(2)=2, b(n) = sum of digits of b(1)+b(2)+b(3)+...+b(n-1), sequence gives values of n such that b(n)=3.

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