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

1,3

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)

Index entries for Colombian or self numbers and related sequences

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): digitsum(n) = local(v, d); v=[]; while(n>0, d=divrem(n, 10); n=d[1]; v=concat(v, d[2])); sum(j=1, matsize(v)[2], v[j]) a065075(m) = local(a, j, s); a=1; print1(a, ", "); s=a; for(j=1, m, a=digitsum(s); print1(a, ", "); s=s+a) a065075(80)
(PARI) SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } { for (n=1, 1000, if (n==1, s=0; a=1, s+=a; a=SumD(s)); write("b065075.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 06 2009
(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

Cf. A004207, A001370, A230289, A001651.

Sequence in context: A153130 A225746 A021406 * A001370 A195715 A343629

Adjacent sequences: A065072 A065073 A065074 * A065076 A065077 A065078

Keyword

nonn,base,easy,look

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