A274515 a(n) is the number of times that the value of ternary n when read as hyperbinary occurs in the set of hyperbinary representations.

1, 1, 2, 2, 1, 3, 3, 2, 3, 3, 2, 3, 3, 1, 4, 4, 3, 5, 4, 3, 5, 5, 2, 5, 5, 3, 4, 4, 3, 5, 5, 2, 5, 5, 3, 4, 5, 3, 4, 4, 1, 5, 5, 4, 7, 5, 4, 7, 7, 3, 8, 8, 5, 7, 5, 4, 7, 7, 3, 8, 8, 5, 7, 8, 5, 7, 7, 2, 7, 7, 5, 8, 7, 5, 8, 8, 3, 7, 7, 4, 5, 5, 4, 7, 7, 3, 8

Offset: 0

Author

Max Barrentine, Jun 25 2016

Keywords

• nonn
• base

Comments

Stern's diatomic sequence A002487 counts the ways (n+1) can be represented if one allows 2's to be included in (n)'s binary representation (its "hyperbinary representations" in the terminology of A002487). A065361 maps ternary ordering onto these hyperbinary representations.

Examples

			5 in ternary is 12, which when read in hyperbinary is equal to 4. 6 in ternary is 20, which when read in hyperbinary is equal to 4. 9 in ternary is 100, which when read in hyperbinary is equal to 4. Since these are the only ways to represent 4 in hyperbinary, a(5) = a(6) = a(9) = 3.
		

Links

• Max Barrentine, Table of n, a(n) for n = 0..9841

Crossrefs

Cf. A002487, A065361.

Formula

a(n) = A002487(A065361(n) + 1).