A249031 The non-anti-Fibonacci numbers: numbers not in A075326.

1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 96, 97, 99, 100

Offset: 1

Author

N. J. A. Sloane, Oct 26 2014

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Wieb Bosma, Rene Bruin, Robbert Fokkink, Jonathan Grube, Anniek Reuijl, and Thian Tromp, Using Walnut to solve problems from the OEIS, arXiv:2503.04122 [math.NT], 2025. See p. 7.
• Robbert Fokkink and Gandhar Joshi, Anti-recurrence sequences, arXiv:2506.13337 [math.NT], 2025. See p. 4.
• D. R. Hofstadter, Anti-Fibonacci numbers, Oct 23 2014
• Thomas Zaslavsky, Anti-Fibonacci Numbers: A Formula, Sep 26 2016

Crossrefs

Cf. A075326, A249032.

Programs

Haskell

import Data.List ((\\))
a249031 n = a249031_list !! (n-1)
a249031_list = f [1..] where
   f ws@(u:v:_) = u : v : f (ws \\ [u, v, u + v])
-- Reinhard Zumkeller, Oct 26 2014

Python

def A249031(n): return n+(n+1-(m:=n-3&7)>>2)+int(m>=4 and (m!=4 or (~((k:=n-3>>3)+1)&k).bit_length()&1)) # Chai Wah Wu, Sep 11 2024