Search: id:A065075
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%I A065075
%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 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)); they end in 
               the cycle {1 2 4 8 7 5}. - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), 
               Dec 11 2005
%C A065075 The missing digital roots are precisely the multiples of 3. - Alexandre 
               Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 28 2005
%C A065075 Conjecture: every non-multiple of 3 does appear in the sequence. - Franklin 
               T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 2009
%H A065075 Harry J. Smith, <a href="b065075.txt">Table of n, a(n) for n=1,...,1000</
               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
%o A065075 (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)
%o A065075 (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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Oct 06 2009]
%Y A065075 Sequence in context: A153130 A029898 A021406 this_sequence A001370 A039794 
               A113417
%Y A065075 Adjacent sequences: A065072 A065073 A065074 this_sequence A065076 A065077 
               A065078
%K A065075 nonn,base,easy
%O A065075 1,3
%A A065075 Bodo Zinser (BodoZinser(AT)Compuserve.com), Nov 09 2001
%E A065075 More terms from Larry Reeves (larryr(AT)acm.org) and Klaus Brockhaus 
               (klaus-brockhaus(AT)t-online.de), Nov 13 2001
%E A065075 Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 
               2009

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