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A073557
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Number of Fibonacci numbers F(k), k <= 10^n, whose initial digit is 1.
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1
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OFFSET
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1,1
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LINKS
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FORMULA
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Limit_{n->infinity} a(n)/10^n = log(2), where the base is 10. - Robert Gerbicz, Sep 05 2002
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EXAMPLE
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a(2) = 30 because there are 30 Fibonacci numbers up to 10^2 whose initial digit is 1.
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PROG
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(PARI) default(realprecision, 10^4); m=log((1+sqrt(5))/2);
lista(nn) = {my(d=log(10)/m, r=log(sqrt(5))/m, s=log(5-sqrt(5))/m, t=0, u=1); for(n=1, nn, u=10*u; while(s<u, if(floor(r+=d)==floor(s+=d), t++, t+=2)); print1(t+(r<u||floor(r)==floor(s)), ", ")); } \\ Jinyuan Wang, Feb 21 2020
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CROSSREFS
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Cf. A000045, A047855 (numbers of integers <= 10^n, whose initial digit is 1).
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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