A026254 a(n) = j if n = [ j*sqrt(3) ], else a(n) = k if n = [ (k/2)*(3 + sqrt(3)) ].

1, 1, 2, 2, 3, 4, 3, 5, 4, 6, 5, 7, 8, 6, 9, 7, 10, 8, 11, 12, 9, 13, 10, 14, 15, 11, 16, 12, 17, 13, 18, 19, 14, 20, 15, 21, 16, 22, 23, 17, 24, 18, 25, 19, 26, 27, 20, 28, 21, 29, 30, 22, 31, 23, 32, 24, 33, 34, 25, 35, 26, 36, 27, 37, 38, 28

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

Every positive integer occurs exactly twice. a(n) is the parent of n in the tree A178528 generated by the Beatty sequence of sqrt(3).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A178528, A022838, A054406.

Programs

Maple

N:= 100: # to get a(1)..a(N)
for j from 1 do m:= floor(j*sqrt(3)); if m > N then break fi; A[m]:= j od:
for k from 1 do m:= floor(k/2*(3+sqrt(3))); if m > N then break fi; A[m]:= k od:
seq(A[i],i=1..N); # Robert Israel, Jan 08 2018

Extensions

Comment by Clark Kimberling, Dec 24 2010