A306441 Next larger integer with same number of runs of 1's in its binary representation as n.

2, 3, 4, 6, 9, 7, 8, 12, 10, 11, 13, 14, 17, 15, 16, 24, 18, 19, 20, 22, 37, 23, 25, 28, 26, 27, 29, 30, 33, 31, 32, 48, 34, 35, 36, 38, 41, 39, 40, 44, 42, 43, 45, 46, 53, 47, 49, 56, 50, 51, 52, 54, 69, 55, 57, 60, 58, 59, 61, 62, 65, 63, 64, 96, 66, 67, 68

Offset: 1

Author

Rémy Sigrist, Feb 15 2019

Keywords

• nonn
• base

Comments

Number of runs of 1's in binary representation is given by A069010.

Each nonnegative number either appears in this sequence or in A002450.

Examples

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   1     2       1         10
   2     3      10         11
   3     4      11        100
   4     6     100        110
   5     9     101       1001
   6     7     110        111
   7     8     111       1000
   8    12    1000       1100
   9    10    1001       1010
  10    11    1010       1011
  11    13    1011       1101
  12    14    1100       1110
  13    17    1101      10001
  14    15    1110       1111
  15    16    1111      10000
  16    24   10000      11000
		

Crossrefs

Cf. A002450, A023758, A043682, A043683, A043684, A043685, A043686, A057168, A069010.

Programs

PARI

r1(n) = my (c=0); while (n, my (v=valuation(n+(n%2),2)); if (n%2, c++); n\=2^v); c
a(n) = my (r=r1(n)); for (k=n+1, oo, if (r==r1(k), return (k)))

Formula

a(A023758(n)) = A023758(n+1) for any n > 1.

a(A043682(n)) = A043682(n+1) for any n > 0.

a(A043683(n)) = A043683(n+1) for any n > 0.

a(A043684(n)) = A043684(n+1) for any n > 0.

a(A043685(n)) = A043685(n+1) for any n > 0.

a(A043686(n)) = A043686(n+1) for any n > 0.