1,3

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

The missing digital roots are precisely the multiples of 3. - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 28 2005

Conjecture: every non-multiple of 3 does appear in the sequence. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 2009

Harry J. Smith, Table of n, a(n) for n=1,...,1000

a(1) = 1, a(2) = 1, a(n) = sum of digits of (a(1)+a(2)+...+a(n-1)).

a(6) = 7 because a(1)+a(2)+a(3)+a(4)+a(5) = 16 and 7 = 1+6

(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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 06 2009]

Sequence in context: A153130 A029898 A021406 this_sequence A001370 A039794 A113417

Adjacent sequences: A065072 A065073 A065074 this_sequence A065076 A065077 A065078

nonn,base,easy

Bodo Zinser (BodoZinser(AT)Compuserve.com), Nov 09 2001

More terms from Larry Reeves (larryr(AT)acm.org) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 13 2001

Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 2009