A381618 Reverse the Chung-Graham representation of n while preserving its trailing zeros: a(n) = A381607(A263273(A381608(n))).
0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 17, 11, 12, 20, 19, 15, 16, 10, 18, 14, 13, 21, 22, 43, 24, 30, 51, 45, 38, 29, 25, 46, 32, 33, 54, 53, 41, 50, 28, 49, 40, 36, 42, 23, 44, 27, 31, 52, 48, 39, 37, 26, 47, 35, 34, 55, 56, 111, 58, 77, 132, 113, 98, 63, 64, 119, 79
Offset: 0
Examples
The first terms, alongside their Chung-Graham representation, are: n a(n) A381579(n) A381579(a(n)) -- ---- ---------- ------------- 0 0 0 0 1 1 1 1 2 2 2 2 3 3 10 10 4 4 11 11 5 7 12 21 6 6 20 20 7 5 21 12 8 8 100 100 9 9 101 101 10 17 102 201 11 11 110 110 12 12 111 111 13 20 112 211 14 19 120 210 15 15 121 121 16 16 200 200
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Programs
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PARI
A381607(n) = { my (t = Vecrev(digits(n, 3))); sum(k = 1, #t, t[k] * fibonacci(2*k)); } A263273(n) = { my (t = 3^if (n, valuation(n, 3), 0)); t * fromdigits(Vecrev(digits(n / t, 3)), 3) } A381608(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););); } a(n) = A381607(A263273(A381608(n)))
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