A306993 -id:A306993 - cp's OEIS frontend

A340258 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n + a(n) is digitally balanced.

1, 7, 6, 5, 4, 3, 2, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 28, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69

Offset: 1

Rémy Sigrist, Jan 02 2021

Digitally balanced numbers correspond to A031443.

This sequence is a self-inverse permutation of the natural numbers.

			The first terms, alongside the binary representation of n + a(n), are:
  n   a(n)  bin(n + a(n))
  --  ----  -------------
   1     1             10
   2     7           1001
   3     6           1001
   4     5           1001
   5     4           1001
   6     3           1001
   7     2           1001
   8    27         100011
   9    26         100011
  10    25         100011
  11    24         100011
  12    23         100011
  13    22         100011

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A340258
Index entries for sequences that are permutations of the natural numbers

Cf. A031443, A306993 (multiplicative variant).

PARI
```
See Links section.
```

def aupto(n):
  alst, aset = [], set()
  for k in range(1, n+1):
    ak = 1
    while True:
      while ak in aset: ak += 1
      binakplusk = bin(ak+k)[2:]
      if binakplusk.count("0")==binakplusk.count("1"): break
      ak += 1
    alst.append(ak)
    aset.add(ak)
  return alst
print(aupto(66)) # Michael S. Branicky, Jan 02 2021

A355642 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the balanced ternary expansion of n * a(n) contains as many negative trits as positive trits.

Original entry on oeis.org

0, 2, 1, 6, 4, 12, 3, 8, 7, 16, 13, 14, 5, 10, 11, 26, 9, 24, 23, 28, 20, 22, 21, 18, 17, 32, 15, 46, 19, 30, 29, 40, 25, 42, 34, 48, 36, 38, 37, 44, 31, 52, 33, 54, 39, 58, 27, 74, 35, 56, 55, 68, 41, 70, 43, 50, 49, 64, 45, 66, 60, 72, 63, 62, 57, 76, 59, 80

Offset: 0

Rémy Sigrist, Jul 11 2022

This sequence is a self-inverse permutation of the nonnegative integers.

			The first terms, alongside the balanced ternary expansion of n * a(n), are:
  n   a(n)  bter(n*a(n))
  --  ----  ------------
   0     0             0
   1     2            1T
   2     1            1T
   3     6          1T00
   4     4          1TT1
   5    12         1T1T0
   6     3          1T00
   7     8         1T01T
   8     7         1T01T
   9    16        1TT100
  10    13        1TTT11
  11    14        1T0T01
  12     5         1T1T0

Rémy Sigrist, Table of n, a(n) for n = 0..2187
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

See A306993 for a similar sequence.

Cf. A065363, A174658, A355639.

PARI
```
See Links section.
```

cp's OEIS Frontend

A340258 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n + a(n) is digitally balanced.

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