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

0,3

Comments

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

Links

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

Formula

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

A381607(a(n)) = n.

Example

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.

Prog

(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); ); ); }

Crossrefs

Cf. A028898, A381579, A381607.

Sequence in context: A013937 A118065 A020661 * A284837 A068937 A285316

Adjacent sequences: A381605 A381606 A381607 * A381609 A381610 A381611

Keyword

nonn,base

Author

Rémy Sigrist, Mar 01 2025

Status

approved