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

%I A340258 #12 Jan 03 2021 09:53:54
%S A340258 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,
%T A340258 9,8,28,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,
%U A340258 88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69
%N A340258 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n + a(n) is digitally balanced.
%C A340258 Digitally balanced numbers correspond to A031443.
%C A340258 This sequence is a self-inverse permutation of the natural numbers.
%H A340258 Rémy Sigrist, <a href="/A340258/b340258.txt">Table of n, a(n) for n = 1..10000</a>
%H A340258 Rémy Sigrist, <a href="/A340258/a340258.gp.txt">PARI program for A340258</a>
%H A340258 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A340258 The first terms, alongside the binary representation of n + a(n), are:
%e A340258   n   a(n)  bin(n + a(n))
%e A340258   --  ----  -------------
%e A340258    1     1             10
%e A340258    2     7           1001
%e A340258    3     6           1001
%e A340258    4     5           1001
%e A340258    5     4           1001
%e A340258    6     3           1001
%e A340258    7     2           1001
%e A340258    8    27         100011
%e A340258    9    26         100011
%e A340258   10    25         100011
%e A340258   11    24         100011
%e A340258   12    23         100011
%e A340258   13    22         100011
%o A340258 (PARI) See Links section.
%o A340258 (Python)
%o A340258 def aupto(n):
%o A340258   alst, aset = [], set()
%o A340258   for k in range(1, n+1):
%o A340258     ak = 1
%o A340258     while True:
%o A340258       while ak in aset: ak += 1
%o A340258       binakplusk = bin(ak+k)[2:]
%o A340258       if binakplusk.count("0")==binakplusk.count("1"): break
%o A340258       ak += 1
%o A340258     alst.append(ak)
%o A340258     aset.add(ak)
%o A340258   return alst
%o A340258 print(aupto(66)) # _Michael S. Branicky_, Jan 02 2021
%Y A340258 Cf. A031443, A306993 (multiplicative variant).
%K A340258 nonn,base
%O A340258 1,2
%A A340258 _Rémy Sigrist_, Jan 02 2021