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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
1, 3, 5, 7, 11, 17, 27, 44, 74, 127, 225, 402, 728, 1333, 2459, 4566, 8525, 15993, 30122, 56936, 107953, 205253, 391223, 747369, 1430648, 2743721, 5270959, 10141978, 19542806, 37708232, 72849931, 140905791, 272836175, 528832794, 1026008203, 1992390617 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..36.

Index entries for Colombian or self numbers and related sequences

EXAMPLE

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

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

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

MAPLE

# A229168, A229169, A229170.

Digits:=24;

log2:=evalf(log(2));

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

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

for i from 2 to 128 do

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

if a >= 2^l then

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

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

od:

lis;

map(floor, lis);

map(ceil, lis);

t1;

PROG

(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 */

CROSSREFS

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

Sequence in context: A024967 A135246 A109543 * A248714 A091567 A241896

Adjacent sequences:  A229165 A229166 A229167 * A229169 A229170 A229171

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 27 2013

EXTENSIONS

a(11)-a(36) from Donovan Johnson, Oct 04 2013

STATUS

approved

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Last modified September 20 10:32 EDT 2019. Contains 327229 sequences. (Running on oeis4.)