OFFSET
1,3
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
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)
FORMULA
a(1) = 1, a(2) = 1, a(n) = sum of digits of (a(1)+a(2)+...+a(n-1)).
EXAMPLE
a(6) = 7 because a(1)+a(2)+a(3)+a(4)+a(5) = 16 and 7 = 1+6.
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
PROG
(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)
(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
CROSSREFS
KEYWORD
AUTHOR
Bodo Zinser, Nov 09 2001
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
STATUS
approved