A088236 - OEIS

%I #31 Jul 21 2024 21:24:32

%S 0,1,2,4,7,10,14,18,23,28,33,39,45,51,57,63,69,76,83,90,97,104,111,

%T 118,125,132,140,148,156,164,172,180,188,196,204,212,220,228,236,244,

%U 252,260,269,278,287,296,305,314,323,332,341,350,359,368,377,386,395

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

%H G. C. Greubel, <a href="/A088236/b088236.txt">Table of n, a(n) for n = 0..5000</a>

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

%p A070939 := n -> `if`(n=0, 1, ilog2(2*n)):

%p A088236 := proc(n) option remember;

%p   if n=0 then 1

%p   else A088236(n-1) + A070939(A088236(n-1)); fi;

%p end proc; # _N. J. A. Sloane_, Aug 30 2022

%t a[n_]:= a[n]= If[n<2, n, a[n-1] + Floor[Log2[a[n-1]]] +1];

%t Table[a[n], {n,0,100}] (* _G. C. Greubel_, Dec 10 2015; Jul 24 2022 *)

%t Join[{0},NestList[#+IntegerLength[#,2]&,1,60]] (* _Harvey P. Dale_, May 14 2024 *)

%o (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

%o (SageMath)

%o @CachedFunction

%o def a(n): return n if (n<2) else a(n-1) + floor(log(a(n-1),2)) + 1 # a = A088236

%o [a(n) for n in (0..100)] # _G. C. Greubel_, Jul 24 2022

%o (Python)

%o from itertools import islice

%o def agen():

%o     yield 0; an = 1

%o     while True: yield an; an += an.bit_length()

%o print(list(islice(agen(), 57))) # _Michael S. Branicky_, Jul 24 2022

%Y Cf. A010062, A070939, A088235.

%K base,easy,nonn

%O 0,3

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