A307294 If n is even, a(n) = A000201(n/2+1), otherwise a(n) = A000201((n-1)/2+1) + 1.

1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 51, 52, 53, 54, 55

Offset: 0

Author

N. J. A. Sloane, Apr 12 2019

Keywords

• nonn

Comments

It follows from the definition that a(2i+1) = a(2i)+1 for all i.

References

• Eric Friedman, Scott M. Garrabrant, Ilona K. Phipps-Morgan, A. S. Landsberg and Urban Larsson, Geometric analysis of a generalized Wythoff game, in Games of no Chance 5, MSRI publ. Cambridge University Press, date? [See Omega, a few lines below Table 2.]

Crossrefs

Cf. A000201, A001950, A307295.

Programs

Python

from math import isqrt
def A307294(n): return ((m:=(n>>1)+1)+isqrt(5*m**2)>>1)+(n&1) # Chai Wah Wu, Aug 10 2022