cp's OEIS Frontend

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

%I A065075 #45 Aug 19 2024 17:10:55
%S A065075 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,
%T A065075 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,
%U A065075 16,14,19,20,13,8,16,14,19,20,22,17,16,14,19,20,13,17,16,14,19,20,13
%N A065075 Sum of digits of the sum of the preceding numbers.
%C A065075 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
%C A065075 The missing digital roots are precisely the multiples of 3. - _Alexandre Wajnberg_, Dec 28 2005
%C A065075 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
%C A065075 a(n) = sum of digits of A004207(n). - _N. J. A. Sloane_, Oct 18 2013
%H A065075 Harry J. Smith and N. J. A. Sloane, <a href="/A065075/b065075.txt">Table of n, a(n) for n = 1..10000</a> (the first 1000 terms were computed by Harry J. Smith)
%H A065075 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F A065075 a(1) = 1, a(2) = 1, a(n) = sum of digits of (a(1)+a(2)+...+a(n-1)).
%e A065075 a(6) = 7 because a(1)+a(2)+a(3)+a(4)+a(5) = 16 and 7 = 1+6.
%p A065075 read transforms;
%p A065075 sp:=1;
%p A065075 lprint(1,sp);
%p A065075 s:=sp;
%p A065075 for n from 2 to 10000 do
%p A065075 sp:=digsum(s);
%p A065075 lprint(n,sp);
%p A065075 s:=s+sp;
%p A065075 od:
%p A065075 # _N. J. A. Sloane_, Oct 17 2013
%o A065075 (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)
%o A065075 a065075(80)
%o A065075 (Haskell)
%o A065075 a065075 n = a065075_list !! (n-1)
%o A065075 a065075_list = 1 : 1 : f 2 where
%o A065075    f x = y : f (x + y) where y = a007953 x
%o A065075 -- _Reinhard Zumkeller_, Nov 13 2014
%Y A065075 Cf. A004207, A001370, A230289, A001651.
%K A065075 nonn,base,easy,look
%O A065075 1,3
%A A065075 _Bodo Zinser_, Nov 09 2001
%E A065075 More terms from Larry Reeves (larryr(AT)acm.org) and _Klaus Brockhaus_, Nov 13 2001
%E A065075 Edited by _Franklin T. Adams-Watters_, Jun 29 2009