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A343852 a(n) is the least k > 0 such that the binary expansions of k and of n + k have the same numbers of 0's and of 1's. 2
5, 10, 9, 20, 21, 18, 17, 40, 19, 42, 38, 36, 37, 34, 33, 80, 35, 38, 37, 84, 35, 76, 74, 72, 73, 74, 70, 68, 69, 66, 65, 160, 67, 70, 69, 76, 67, 74, 73, 168, 75, 70, 69, 152, 67, 148, 146, 144, 71, 146, 145, 148, 140, 140, 138, 136, 137, 138, 134, 132, 133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the binary analog of A343888.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..8191

FORMULA

a(n) <= A004757(n).

EXAMPLE

The first terms, alongside the binary expansions of a(n) and of n + a(n), are:

n a(n) bin(a(n)) bin(n+a(n))

-- ---- --------- -----------

1 5 101 110

2 10 1010 1100

3 9 1001 1100

4 20 10100 11000

5 21 10101 11010

6 18 10010 11000

7 17 10001 11000

8 40 101000 110000

9 19 10011 11100

10 42 101010 110100

11 38 100110 110001

12 36 100100 110000

13 37 100101 110010

14 34 100010 110000

15 33 100001 110000

PROG

(PARI) a(n) = { for (k=1, oo, if (#binary(k)==#binary(n+k) && hammingweight(k)==hammingweight(n+k), return (k))) }

(Python)

def a(n):

k = 1

while k.bit_length() != (n+k).bit_length() or bin(k).count('1') != bin(n+k).count('1'): k += 1

return k

print([a(n) for n in range(1, 62)]) # Michael S. Branicky, May 04 2021

CROSSREFS

Cf. A000120, A004757, A023416, A293198, A343888.

Sequence in context: A109360 A141622 A144136 * A198286 A001483 A173679

Adjacent sequences: A343849 A343850 A343851 * A343853 A343854 A343855

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, May 03 2021

STATUS

approved

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Last modified November 27 19:48 EST 2022. Contains 358406 sequences. (Running on oeis4.)