A341944 Next larger integer with same number of runs in binary expansion as n.

3, 4, 7, 6, 9, 8, 15, 12, 11, 18, 13, 14, 17, 16, 31, 24, 19, 20, 23, 22, 37, 26, 25, 28, 27, 34, 29, 30, 33, 32, 63, 48, 35, 36, 39, 38, 41, 40, 47, 44, 43, 74, 45, 46, 53, 50, 49, 56, 51, 52, 55, 54, 69, 58, 57, 60, 59, 66, 61, 62, 65, 64, 127, 96, 67, 68

Offset

1,1

Comments

Number of runs in binary expansion is given by A005811.

This is a permutation of A107907.

Links

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

Index entries for sequences related to binary expansion of n

Formula

A005811(a(n)) = A005811(n).

a(2^k-1) = 2^(k+1)-1 for any k > 0.

Example

The first terms in decimal and in binary, alongside A005811(n), are:
  n   a(n)  bin(n)  bin(a(n))  A005811(n)
  --  ----  ------  ---------  ----------
   1     3       1         11           1
   2     4      10        100           2
   3     7      11        111           1
   4     6     100        110           2
   5     9     101       1001           3
   6     8     110       1000           2
   7    15     111       1111           1
   8    12    1000       1100           2
   9    11    1001       1011           3
  10    18    1010      10010           4
  11    13    1011       1101           3
  12    14    1100       1110           2

Prog

(PARI) a(n) = my (r=hammingweight(bitxor(n, n>>1))); for (k=n+1, oo, if (r==hammingweight(bitxor(k, k>>1)), return (k)))
(Python)
def runs(n): return bin(n^(n>>1)).count('1')
def a(n):
  nruns, m = runs(n), n + 1
  while runs(m) != nruns: m += 1
  return m
print([a(n) for n in range(1, 67)]) # Michael S. Branicky, Feb 24 2021

Crossrefs

Cf. A000975, A005811, A057168, A107907.

Sequence in context: A096842 A147966 A351923 * A332994 A086469 A087030

Adjacent sequences: A341941 A341942 A341943 * A341945 A341946 A341947

Keyword

nonn,base

Author

Rémy Sigrist, Feb 24 2021

Status

approved