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 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 (list; graph; refs; listen; history; text; internal format)
 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): 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

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Last modified May 9 17:48 EDT 2021. Contains 343742 sequences. (Running on oeis4.)