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A340258 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n + a(n) is digitally balanced. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Digitally balanced numbers correspond to A031443.
This sequence is a self-inverse permutation of the natural numbers.
LINKS
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: A333884 A055118 A132671 * A074921 A182209 A120634
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 02 2021
STATUS
approved

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Last modified June 16 15:23 EDT 2024. Contains 373432 sequences. (Running on oeis4.)