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

Author

Rémy Sigrist, Jan 02 2021

Keywords

• nonn
• base

Comments

Digitally balanced numbers correspond to A031443.

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

Examples

			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
		

Links

• 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

Crossrefs

Cf. A031443, A306993 (multiplicative variant).

Programs

PARI

See Links section.

Python

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