

A065075


Sum of digits of the sum of the preceding numbers.


20



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
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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 nonmultiple of 3 does appear in the sequence.  Franklin T. AdamsWatters, 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(n1)).


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+=x10*(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 !! (n1)
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 A039794
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. AdamsWatters, Jun 29 2009


STATUS

approved



