A054084 Permutation of N: for each k >= 1, let p(k)=least natural number not already an a(i), q(k)=p(k)+k, a(2k-1)=q(k), a(2k)=p(k).

2, 1, 5, 3, 7, 4, 10, 6, 13, 8, 15, 9, 18, 11, 20, 12, 23, 14, 26, 16, 28, 17, 31, 19, 34, 21, 36, 22, 39, 24, 41, 25, 44, 27, 47, 29, 49, 30, 52, 32, 54, 33, 57, 35, 60, 37, 62, 38, 65, 40, 68, 42, 70, 43, 73, 45, 75, 46, 78, 48, 81, 50, 83

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• eigen

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A054082, A054085.

Odd-indexed terms: A001950 (Upper Wythoff sequence). Even-indexed terms: A000201 (Lower Wythoff sequence). Inverse permutation: A064786.

Programs

Python

from math import isqrt
def A054084(n): return ((m:=n+1>>1)+isqrt(5*m**2)>>1)+m*(n&1) # Chai Wah Wu, Aug 25 2022