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 A374962 #17 Aug 17 2024 03:22:07 %S A374962 1,3,4,7,8,13,14,20,26,50,55,58,90,140,270,314,603 %N A374962 Numbers k such that the number of terms in the Zeckendorf representation of 2^k equals the binary weight of Fibonacci(k). %C A374962 Numbers k such that A007895(A000079(k)) = A000120(A000045(k)), or equivalently A020908(k) = A011373(k). %C A374962 The corresponding values of A020908(k) = A011373(k) are 1, 1, 2, 3, 3, 5, 6, 8, 9, 18, 22, 24, 33, 53, 106, 122, 232, ... . %C A374962 a(18) > 63000, if it exists. %C A374962 a(18) > 333333, if it exists. - _Lucas A. Brown_, Aug 13 2024 %H A374962 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A374962.py">Python program</a>. %e A374962 n | k = a(n) | 2^k | A014417(2^k) | F(k) | A007088(F(k)) | Number of 1's %e A374962 --+----------+-----+--------------+------+---------------+-------------- %e A374962 1 | 1 | 2 | 10 | 1 | 1 | 1 %e A374962 2 | 3 | 8 | 10000 | 2 | 10 | 1 %e A374962 3 | 4 | 16 | 100100 | 3 | 11 | 2 %e A374962 4 | 7 | 128 | 1010001000 | 13 | 1101 | 3 %e A374962 5 | 8 | 256 | 100001000010 | 21 | 10101 | 3 %t A374962 z[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; (* _Alonso del Arte_ at A007895 *) %t A374962 Select[Range[700], z[2^#] == DigitCount[Fibonacci[#], 2, 1] &] %o A374962 (PARI) A007895(n)=if(n<4, n>0, my(k=2, s, t); while(fibonacci(k++)<=n, ); while(k && n, t=fibonacci(k); if(t<=n, n-=t; s++); k--); s); \\ _Charles R Greathouse IV_ at A007895 %o A374962 is(k) = A007895(2^k) == hammingweight(fibonacci(k)); %Y A374962 Cf. A000045, A000079, A000120, A007088, A007895, A011373, A014417, A020908. %K A374962 nonn,base,more %O A374962 1,2 %A A374962 _Amiram Eldar_, Jul 25 2024