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%I #4 Apr 02 2014 15:42:29
%S 1,2,4,8,16,32,55,83,121,170,232,302,379,470,571,674,781,896,1018,
%T 1145,1282,1430,1591,1760,1945,2144,2362,2591,2833,3083,3340,3611,
%U 3892,4184,4489,4802,5122,5447,5782,6128,6487,6863,7255,7661,8077,8504,8944,9392
%N Partial sums of A004207.
%C Partial sums of a(1) = 1, a(n) = sum of digits of all previous terms. The subsequence of primes in this sequence begins: 2, 83, 379, 571, 2591, 2833, 3083, 6863, 10831. The subsequence of squares in this sequence begins: 1, 4, 16, 121, 4489.
%F a(n) = SUM[i=0..n] A004207(i) = SUM[i=0..n] {b(1) = 1, b(j) = sum of digits of b(j) for j = 0..i} = SUM[i=0..n] {b(1) = 1, b(k) = A007953(b(k)) for k = 0..i}.
%e a(7) = 1 + 1 + 2 + 4 + 8 + 16 + 23 + 28 = 83 is prime.
%p A176718 := proc(n)
%p add( A004207(k),k=0..n) ;
%p end proc: # _R. J. Mathar_, Apr 02 2014
%Y Cf. A004207, A016052, A033298, A007612.
%K base,easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Apr 25 2010
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