A381608 Nonnegative integers whose ternary expansion does not contain pairs of 2's only separated by (zero or more) 1's, with offset 0.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93

Offset: 0

Author

Rémy Sigrist, Mar 01 2025

Keywords

• nonn
• base

Comments

The ternary expansion of a(n) equals the decimal expansion of A381579(n).

Examples

			The ternary expansion of 20, "211", has no pairs of 2's, so 20 belongs to the sequence.The ternary expansion of 21, "212", has a pair of 2s only separated by 1's, so 21 does not belong to the sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560

Crossrefs

Cf. A028898, A381579, A381607.

Programs

PARI

a(n) = { for (k = 1, oo, my (f = fibonacci(2*k)); if (f >= n, my (v = 0); while (n, while (n >= f, n -= f; v += 3^(k-1);); f = fibonacci(2*k--);); return (v););); }

Formula

a(n) = A028898(A381579(n)).

A381607(a(n)) = n.