cp's OEIS Frontend

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.

A114477 Smallest Fibonacci number with Hamming weight n (i.e., smallest number with exactly n ones when written in binary), or -1 if no such number exists.

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%I A114477 #22 Jul 29 2025 10:27:52
%S A114477 0,1,3,13,89,55,377,1597,987,121393,39088169,28657,514229,3524578,
%T A114477 24157817,1134903170,102334155,165580141,701408733,2504730781961,
%U A114477 956722026041,1836311903,139583862445,6557470319842,591286729879,17167680177565,4052739537881,806515533049393
%N A114477 Smallest Fibonacci number with Hamming weight n (i.e., smallest number with exactly n ones when written in binary), or -1 if no such number exists.
%C A114477 Among the first 10^5 Fibonacci numbers, none have Hamming weight 44, 45, 61, 62, 76, 92, or 95. - _T. D. Noe_, Jun 25 2007
%H A114477 Amiram Eldar, <a href="/A114477/b114477.txt">Table of n, a(n) for n = 0..43</a>
%F A114477 a(n) = MIN{A000045(k): A000120(A000045(k)) = n}.
%t A114477 a[ n_ ] := Module[ {}, k = 0; While[ Not[ Plus @@ IntegerDigits[ Fibonacci[ k ], 2 ] == n ], k++ ]; Fibonacci[ k ] ]; Table[ a[ i ], {i, 0, 40} ] (* _Stefan Steinerberger_ *)
%Y A114477 Cf. A000045, A000120, A011373.
%K A114477 nonn,base
%O A114477 0,3
%A A114477 _Jonathan Vos Post_, Jun 24 2007
%E A114477 Extended by _Stefan Steinerberger_, Jun 25 2007