A065075 Sum of digits of the sum of the preceding numbers.

1, 1, 2, 4, 8, 7, 5, 10, 11, 13, 8, 7, 14, 10, 2, 4, 8, 7, 5, 10, 11, 13, 8, 16, 14, 19, 11, 13, 8, 7, 14, 10, 11, 13, 8, 7, 5, 10, 11, 13, 17, 16, 14, 10, 11, 13, 8, 16, 14, 19, 20, 13, 8, 16, 14, 19, 20, 13, 8, 16, 14, 19, 20, 22, 17, 16, 14, 19, 20, 13, 17, 16, 14, 19, 20, 13

Offset: 1

Author

Bodo Zinser, Nov 09 2001

Keywords

• nonn
• base
• easy
• look

Comments

This sequence has the same digital roots as A004207 (a(1) = 1, a(n) = sum of digits of all previous terms) and A001370 (Sum of digits of 2^n); the digital roots sequence ends in the cycle {1 2 4 8 7 5}. - Alexandre Wajnberg, Dec 11 2005

The missing digital roots are precisely the multiples of 3. - Alexandre Wajnberg, Dec 28 2005

Conjecture: every non-multiple of 3 does appear in the sequence. - Franklin T. Adams-Watters, Jun 29 2009. See A230289. - N. J. A. Sloane, Oct 17 2013

a(n) = sum of digits of A004207(n). - N. J. A. Sloane, Oct 18 2013

Examples

			a(6) = 7 because a(1)+a(2)+a(3)+a(4)+a(5) = 16 and 7 = 1+6.
		

Links

• Harry J. Smith and N. J. A. Sloane, Table of n, a(n) for n = 1..10000 (the first 1000 terms were computed by Harry J. Smith)
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A004207, A001370, A230289, A001651.

Programs

Haskell

a065075 n = a065075_list !! (n-1)
a065075_list = 1 : 1 : f 2 where
   f x = y : f (x + y) where y = a007953 x
-- Reinhard Zumkeller, Nov 13 2014

Maple

read transforms;
sp:=1;
lprint(1,sp);
s:=sp;
for n from 2 to 10000 do
sp:=digsum(s);
lprint(n,sp);
s:=s+sp;
od:
# N. J. A. Sloane, Oct 17 2013

PARI

a065075(m) = local(a,j,s); a=1; print1(a,", "); s=a; for(j=1,m,a=sumdigits(s); print1(a,", "); s=s+a)
a065075(80)

Formula

a(1) = 1, a(2) = 1, a(n) = sum of digits of (a(1)+a(2)+...+a(n-1)).

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Klaus Brockhaus, Nov 13 2001

Edited by Franklin T. Adams-Watters, Jun 29 2009