A381625 -id:A381625 - cp's OEIS frontend

A381627 Irregular table T(n, k), n >= 0, k = 1..A381625(n): the n-th row lists the numbers m such that A381624(m) = n.

0, 1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 11, 12, 13, 14, 15, 16, 18, 17, 19, 27, 20, 28, 21, 29, 22, 30, 23, 31, 24, 32, 25, 33, 26, 34, 36, 35, 37, 38, 39, 40, 41, 42, 43, 45, 44, 46, 54, 47, 55, 81, 48, 56, 82, 49, 57, 83, 50, 58, 84, 51, 59, 85, 52, 60, 86, 53, 61, 63, 87

Offset: 0

Rémy Sigrist, Mar 02 2025

As a flat sequence, this is a permutation of the nonnegative integers with inverse A381628.

			Table T(n, k) begins:
  n   n-th row
  --  ----------
   0  0
   1  1
   2  2
   3  3
   4  4
   5  5
   6  6
   7  7, 9
   8  8, 10
   9  11
  10  12
  11  13
  12  14
  13  15
  14  16, 18
  15  17, 19, 27
  16  20, 28

Rémy Sigrist, Table of n, a(n) for n = 0..9890
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A381624, A381625, A381628 (inverse).

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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).

Original entry on oeis.org

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

Rémy Sigrist, Mar 02 2025

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

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

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

Cf. A354047, A381625.

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

a(A354047(n)) = n.

cp's OEIS Frontend

A381627 Irregular table T(n, k), n >= 0, k = 1..A381625(n): the n-th row lists the numbers m such that A381624(m) = n.

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