This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038546 #26 Feb 16 2025 08:32:38
%S A038546 0,1,5,43,48,53,3301,48515,348422,406665,1200207,6698641,190821326,
%T A038546 2292141445,257125021372,5843866639660,45173327533483,46312809996150,
%U A038546 59358981837795,129408997210988,1450344802530203,5710154240910003
%N A038546 Numbers n such that n-th Fibonacci number has initial digits n.
%C A038546 The Mathematica coding used by _Robert G. Wilson v_ implements Binet's Fibonacci number formula as suggested by _David W. Wilson_ and incorporates _Benoit Cloitre_'s use of logarithms to achieve a further increase in speed.
%C A038546 Fixed points of A020344. - _Alois P. Heinz_, Jul 08 2022
%H A038546 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html">Fibonacci Numbers and the Golden Section</a>
%H A038546 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci numbers</a>
%F A038546 n>5 is in the sequence if a=(1+sqrt(5))/2 b=1/sqrt(5) and n==floor(b*(a^n)/10^(floor((log(b) +n*log(a))/log(10))-floor(log(n)/log(10))) ). - _Benoit Cloitre_, Feb 27 2002
%e A038546 a(3)=43 since 43rd Fibonacci number starts with 43 -> {43}3494437.
%e A038546 Fibonacci(53) is 53316291173, which begins with 53, so 53 is a term in the sequence.
%t A038546 a = N[ Log[10, Sqrt[5]/5], 24]; b = N [Log[10, GoldenRatio], 24]; Do[ If[ IntegerPart[10^FractionalPart[a + n*b]*10^Floor[ Log[10, n]]] == n, Print[n]], {n, 225000000}] (* _Robert G. Wilson v_, May 09 2005 *)
%t A038546 (* confirmed with: *) fQ[n_] := (FromDigits[ Take[ IntegerDigits[ Fibonacci[n]], Floor[ Log[10, n] + 1]]] == n)
%o A038546 (PARI) /* To obtain terms > 5: */ a=(1+sqrt(5))/2; b=1/sqrt(5); for(n=1,3500, if(n==floor(b*(a^n)/10^( floor(log(b *(a^n))/log(10))-floor(log(n)/log(10)))),print1(n,","))) \\ _Benoit Cloitre_, Feb 27 2002
%Y A038546 Cf. A000045, A020344, A052000, A000350, A050816.
%K A038546 nonn,base,nice
%O A038546 1,3
%A A038546 _Jeff Burch_
%E A038546 Term a(6) from _Patrick De Geest_, Oct 15 1999
%E A038546 a(7) from _Benoit Cloitre_, Feb 27 2002
%E A038546 a(8)-a(11) from _Robert G. Wilson v_, May 09 2005
%E A038546 a(12) from _Robert G. Wilson v_, May 11 2005
%E A038546 More terms from _Robert Gerbicz_, Aug 22 2006