cp's OEIS Frontend

A229168 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = smallest i such that b(i) >= 2^n.

%I A229168 #25 Nov 05 2013 20:12:06
%S A229168 1,3,5,7,11,17,27,44,74,127,225,402,728,1333,2459,4566,8525,15993,
%T A229168 30122,56936,107953,205253,391223,747369,1430648,2743721,5270959,
%U A229168 10141978,19542806,37708232,72849931,140905791,272836175,528832794,1026008203,1992390617
%N A229168 Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = smallest i such that b(i) >= 2^n.
%H A229168 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A229168 The initial terms of the b(n) sequence are approximately
%e A229168 2, 3.00000000000000000000000, 4.58496250072115618145375, 6.78187243514238888864578, 9.54355608312733448665509, 12.7980830210090262451102, 16.4759388461842196480290, 20.5182276175427023220954, 24.8770618274970204646817, 29.5138060245244394221195, 34.3971240984210783617324, ...
%e A229168 b(5) is the first term >= 8, so a(3) = 5.
%p A229168 # A229168, A229169, A229170.
%p A229168 Digits:=24;
%p A229168 log2:=evalf(log(2));
%p A229168 lis:=[2]; a:=2;
%p A229168 t1:=[1]; l:=2;
%p A229168 for i from 2 to 128 do
%p A229168 a:=evalf(a+log(a)/log2);
%p A229168 if a >= 2^l then
%p A229168 l:=l+1; t1:=[op(t1),i]; fi;
%p A229168 lis:=[op(lis),a];
%p A229168 od:
%p A229168 lis;
%p A229168 map(floor,lis);
%p A229168 map(ceil,lis);
%p A229168 t1;
%o A229168 (PARI) n=1; p2=2^n; m=2; lg2=log(2); for(i=1, 1992390617, if(m>=p2, print(n " " i); n++; p2=2^n); m=m+log(m)/lg2) /* _Donovan Johnson_, Oct 04 2013 */
%Y A229168 Cf. A229169, A229170, A010062, A229167, A155921, A229177; also A004207, A229171, A229172, A229173.
%K A229168 nonn
%O A229168 1,2
%A A229168 _N. J. A. Sloane_, Sep 27 2013
%E A229168 a(11)-a(36) from _Donovan Johnson_, Oct 04 2013