A088235 Total number of digits (in base 10) in all preceding terms in the sequence.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

a(n+1) = a(n) + floor(Log(10, a(n))) + 1, with a(0) = 0, a(1) = 1.

a(n) = A064223(n), n>0. - R. J. Mathar, Sep 11 2008

Mathematica

a[n_]:= a[n]= If[n<2, n, a[n-1] +Floor[Log10[a[n-1]]] +1];
Table[a[n], {n, 0, 100}] (* G. C. Greubel, Dec 10 2015; Jul 24 2022 *)

Prog

(PARI) lista(nn) = {ns = 0; v = vector(nn); for (i=2, nn, ns += #Str(v[i-1]); v[i] = ns; ); v; } \\ Michel Marcus, Dec 05 2015
(SageMath)
@CachedFunction
def a(n): return n if (n<2) else a(n-1) + floor(log(a(n-1), 10)) + 1 # a = A088235
[a(n) for n in (0..100)] # G. C. Greubel, Jul 24 2022
(Python)
from itertools import islice
def agen():
    an = 0
    while True: yield an; an += len(str(an))
print(list(islice(agen(), 67))) # Michael S. Branicky, Jul 26 2022

Crossrefs

Cf. A064223, A088236.

Sequence in context: A102685 A032960 A117804 * A064223 A098952 A144688

Adjacent sequences: A088232 A088233 A088234 * A088236 A088237 A088238

Keyword

base,easy,nonn

Author

David Corbett (dcorbett42(AT)yahoo.co.nz), Sep 25 2003

Extensions

More terms from Alexandre Wajnberg, Jan 02 2006

Status

approved