A219675 Starting with a(0)=0, a(n) = 1 + the sum of the digital sums of a(0) through a(n-1).

0, 1, 2, 4, 8, 16, 23, 28, 38, 49, 62, 70, 77, 91, 101, 103, 107, 115, 122, 127, 137, 148, 161, 169, 185, 199, 218, 229, 242, 250, 257, 271, 281, 292, 305, 313, 320, 325, 335, 346, 359, 376, 392, 406, 416, 427, 440, 448, 464, 478, 497, 517, 530, 538, 554, 568

Offset: 0

Author

Bob Selcoe, Nov 17 2014

Keywords

• nonn
• base
• easy

Comments

Almost identical to A004207, only difference being a(0). - Yuval Filmus, Apr 22 2016.

Examples

			a(7) = 28 because (0+1+2+4+8+1+6+2+3) + 1 = 28.
		

Links

• Eric Angelini, a(n) > cumulative sum of digits, Seqfan, Nov. 11, 2014.

Crossrefs

Cf. A004207 (essentially the same), A007953 (sum of digits), A244510 (related).

Programs

Mathematica

a219675[n_Integer] := Module[{f}, f[0] = 0; f[k_] := 1 + Sum[Plus @@ IntegerDigits[f[i]], {i, 0, k - 1}]; f[n]]; a219675/@Range[40] (* Michael De Vlieger, Nov 17 2014 *)

PARI

lista(nn) = {v = vector(nn); for (n=2, nn, v[n] = 1 + sum(k=1, n-1, sumdigits(v[k])););v;} \\ Michel Marcus, Nov 17 2014

PARI

A219675_upto(n)=vector(n,i,n=if(i<3, i-1, n+sumdigits(n))) \\ M. F. Hasler, Oct 30 2024

Formula

a(n) = Sum_{k=0..n-1} digsum(a(k)) + 1.

a(n) = a(n-1) + digsum(a(n-1)).

Extensions

More terms from Michel Marcus, Nov 17 2014