A249032 First differences of A075326.

3, 6, 4, 5, 5, 6, 4, 6, 4, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 6, 4, 6, 4, 5, 5, 6, 4, 6, 4, 6, 4, 5, 5, 6, 4, 6, 4, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 6, 4, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 6, 4, 6, 4, 5, 5, 6, 4, 5, 5, 6, 4, 5, 5, 6

Offset: 0

Author

N. J. A. Sloane, Oct 26 2014

Keywords

• nonn

Comments

Can be constructed as follows. Apart from the initial "3", one always has either "6-4" (i.e., a 6 followed by a 4), or else "5-5". The 6-4's always come either alone (6-4) or triply (6-4, 6-4, 6-4), while the 5-5's always come alone. So if we let "6-4, 5-5" be represented by the numeral "1", and "6-4, 6-4, 6-4, 5-5" by the numeral "3", then the sequence of first differences, in this compressed code, is A080426, which itself is defined by a simple substitution rule. - D. R. Hofstadter, Oct 23 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Robbert Fokkink and Gandhar Joshi, Anti-recurrence sequences, arXiv:2506.13337 [math.NT], 2025. See pp. 2, 18.
• D. R. Hofstadter, Anti-Fibonacci numbers, Oct 23 2014
• Thomas Zaslavsky, Anti-Fibonacci Numbers: A Formula, Sep 26 2016

Crossrefs

Cf. A075326, A080426, A249031.

Programs

Haskell

a249032 n = a249032_list !! n
a249032_list = zipWith (-) (tail a075326_list) a075326_list
-- Reinhard Zumkeller, Oct 26 2014

Python

def A249032(n): return 4+int((n+1|(~((m:=n>>1)+1)&m).bit_length())&1^1)+int((n|(~((k:=n-1>>1)+1)&k).bit_length())&1) if n else 3 # Chai Wah Wu, Sep 11 2024