A088236 Total number of digits (in base 2) in all preceding terms in the sequence.

0, 1, 2, 4, 7, 10, 14, 18, 23, 28, 33, 39, 45, 51, 57, 63, 69, 76, 83, 90, 97, 104, 111, 118, 125, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 269, 278, 287, 296, 305, 314, 323, 332, 341, 350, 359, 368, 377, 386, 395

Offset

0,3

Links

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

Formula

a(n+1) = a(n) + floor(Log(2, a(n))) + 1, with a(0) = 0, a(1) = 1.

Maple

A070939 := n -> `if`(n=0, 1, ilog2(2*n)):
A088236 := proc(n) option remember;
  if n=0 then 1
  else A088236(n-1) + A070939(A088236(n-1)); fi;
end proc; # N. J. A. Sloane, Aug 30 2022

Mathematica

a[n_]:= a[n]= If[n<2, n, a[n-1] + Floor[Log2[a[n-1]]] +1];
Table[a[n], {n, 0, 100}] (* G. C. Greubel, Dec 10 2015; Jul 24 2022 *)
Join[{0}, NestList[#+IntegerLength[#, 2]&, 1, 60]] (* Harvey P. Dale, May 14 2024 *)

Prog

(PARI) alist(n) = my(r=vector(n), val=0, delta=1, pow=2); for(i=2, n, r[i]=val+=delta; if(val>=pow, delta++; pow*=2)); r \\ Franklin T. Adams-Watters, Oct 11 2014
(SageMath)
@CachedFunction
def a(n): return n if (n<2) else a(n-1) + floor(log(a(n-1), 2)) + 1 # a = A088236
[a(n) for n in (0..100)] # G. C. Greubel, Jul 24 2022
(Python)
from itertools import islice
def agen():
    yield 0; an = 1
    while True: yield an; an += an.bit_length()
print(list(islice(agen(), 57))) # Michael S. Branicky, Jul 24 2022

Crossrefs

Cf. A010062, A070939, A088235.

Sequence in context: A225249 A214048 A328659 * A194244 A014616 A184674

Adjacent sequences: A088233 A088234 A088235 * A088237 A088238 A088239

Keyword

base,easy,nonn

Author

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

Status

approved