A176718 Partial sums of A004207.

1, 2, 4, 8, 16, 32, 55, 83, 121, 170, 232, 302, 379, 470, 571, 674, 781, 896, 1018, 1145, 1282, 1430, 1591, 1760, 1945, 2144, 2362, 2591, 2833, 3083, 3340, 3611, 3892, 4184, 4489, 4802, 5122, 5447, 5782, 6128, 6487, 6863, 7255, 7661, 8077, 8504, 8944, 9392

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

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.

Examples

			a(7) = 1 + 1 + 2 + 4 + 8 + 16 + 23 + 28 = 83 is prime.
		

Crossrefs

Cf. A004207, A016052, A033298, A007612.

Programs

Maple

A176718 := proc(n)
    add( A004207(k),k=0..n) ;
end proc: # R. J. Mathar, Apr 02 2014

Formula

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}.