A381624 For any nonnegative integer n with ternary expansion Sum_{k >= 0} t_k * 3^k, a(n) = Sum_{k >= 0} t_k * (2^(k+1) - 1).

0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 19, 20, 21, 22, 15, 16, 17, 18, 19, 20, 21, 22, 23, 22, 23, 24, 25, 26, 27, 28, 29, 30, 29, 30, 31, 32, 33, 34, 35, 36, 37, 30, 31, 32, 33, 34, 35, 36, 37, 38, 37, 38, 39, 40, 41

Offset: 0

Author

Rémy Sigrist, Mar 02 2025

Keywords

• nonn
• base
• easy

Comments

Every nonnegative integer appears in the sequence, a finite number of times.

Examples

			a(42) = a(3^3 + 3^2 + 2*3) = (2^(3+1) - 1) + (2^(2+1) - 1) + 2*(2^(1+1) - 1) = 28.
		

Links

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

Crossrefs

Cf. A354047, A381625.

Programs

PARI

a(n) = { my (v = 0, k); while (n, n -= 3^k = valuation(n, 3); v += 2^(k+1) - 1;); return (v); }

Formula

a(A354047(n)) = n.