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.
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
Offset: 1
Keywords
Examples
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.
Crossrefs
Programs
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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;
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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 */
Extensions
a(11)-a(36) from Donovan Johnson, Oct 04 2013
Comments