A084228 a(1)=1, a(2)=2; thereafter a(n) = sum of digits of (a(1)+a(2)+a(3)+...+a(n-1)).

1, 2, 3, 6, 3, 6, 3, 6, 3, 6, 12, 6, 12, 15, 12, 15, 3, 6, 3, 6, 12, 6, 12, 15, 12, 15, 3, 6, 3, 6, 12, 6, 12, 15, 12, 15, 12, 6, 12, 6, 12, 15, 12, 15, 12, 15, 12, 6, 12, 15, 12, 15, 12, 15, 12, 15, 12, 15, 12, 15, 21, 15, 12, 15, 12, 15, 21, 24, 12, 15, 12, 15, 21, 24, 12, 15, 21, 15

Offset: 1

Author

Benoit Cloitre, Jun 21 2003

Keywords

• base
• nonn

Comments

a(n) == 3 or 6 (mod 9) n>2.

a(n) = 3 for n in A084229.

a(n) = 6 for n = 4, 6, 8, 10, 12, 18, 20, 22, 28, 30, 32, 38, 40, 48, 86, 88, 90, 96, 98, 100, 106, 108, 116, 160, 162, 168, 170, 178, ..., 17630. - Robert G. Wilson v, Jun 27 2014

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A065075, A016052, A230286, A230287, A004207, A084229.

Programs

Haskell

a084228 n = a084228_list !! (n-1)
a084228_list = 1 : 2 : f 3 where
   f x = y : f (x + y) where y = a007953 x
-- Reinhard Zumkeller, Nov 13 2014

Mathematica

a[1] = 1; a[2] = 2; a[n_] := a[n] = Sum[ Total@ IntegerDigits@ a@ i, {i, n - 1}]; Array[ Total@ IntegerDigits@ a@# &, 78] (* Robert G. Wilson v, Jun 27 2014 *)
nxt[{t_,a_}]:=Module[{c=Total[IntegerDigits[t]]},{t+c,c}]; Join[{1},NestList[nxt,{3,2},80][[;;,2]]] (* Harvey P. Dale, Jul 13 2023 *)

PARI

sumdig(n)=sum(k=0,ceil(log(n)/log(10)),floor(n/10^k)%10)
an=vector(10000); a(n)=if(n<0,0,an[n])
an[1]=1; an[2]=2; for(n=3,300,an[n]=sumdig(sum(k=1,n-1,a(k))))