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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. 6

%I

%S 1,3,5,7,11,17,27,44,74,127,225,402,728,1333,2459,4566,8525,15993,

%T 30122,56936,107953,205253,391223,747369,1430648,2743721,5270959,

%U 10141978,19542806,37708232,72849931,140905791,272836175,528832794,1026008203,1992390617

%N 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 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%e The initial terms of the b(n) sequence are approximately

%e 2, 3.00000000000000000000000, 4.58496250072115618145375, 6.78187243514238888864578, 9.54355608312733448665509, 12.7980830210090262451102, 16.4759388461842196480290, 20.5182276175427023220954, 24.8770618274970204646817, 29.5138060245244394221195, 34.3971240984210783617324, ...

%e b(5) is the first term >= 8, so a(3) = 5.

%p # A229168, A229169, A229170.

%p Digits:=24;

%p log2:=evalf(log(2));

%p lis:=[2]; a:=2;

%p t1:=[1]; l:=2;

%p for i from 2 to 128 do

%p a:=evalf(a+log(a)/log2);

%p if a >= 2^l then

%p l:=l+1; t1:=[op(t1),i]; fi;

%p lis:=[op(lis),a];

%p od:

%p lis;

%p map(floor,lis);

%p map(ceil,lis);

%p t1;

%o (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 Cf. A229169, A229170, A010062, A229167, A155921, A229177; also A004207, A229171, A229172, A229173.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Sep 27 2013

%E a(11)-a(36) from _Donovan Johnson_, Oct 04 2013

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Last modified October 15 10:15 EDT 2019. Contains 328026 sequences. (Running on oeis4.)