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

1,2

Comments

Digitally balanced numbers correspond to A031443.

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

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

Example

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

Prog

(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

Crossrefs

Cf. A031443, A306993 (multiplicative variant).

Sequence in context: A055118 A375147 A132671 * A074921 A182209 A120634

Adjacent sequences: A340255 A340256 A340257 * A340259 A340260 A340261

Keyword

nonn,base

Author

Rémy Sigrist, Jan 02 2021

Status

approved