A374348 a(n) = k where wt(k) = n and k + wt(k) = a power of two, where wt(n) = A000120(n) = binary weight of n.

1, 6, 13, 60, 59, 250, 505, 2040, 1015, 4086, 8181, 32756, 32755, 131058, 262129, 1048560, 262127, 1048558, 2097133, 8388588, 8388587, 33554410, 67108841, 268435432, 134217703, 536870886, 1073741797, 4294967268, 4294967267, 17179869154, 34359738337, 137438953440

Offset

1,2

Comments

k is uniquely determined by finding the power of two for which k = 2^x - n has wt(k) = n.

Terms are not always increasing, since the number of 0 bits in n-1 reduces k.

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = 2^A230300(n) - n.

a(n) = 2^(n + A000120(n-1)) - n.

a(n) = 2 * A129195(n-1) - n.

a(n) == n (mod 2).

Example

For n = 4, 60 in binary is 111100, which has sum of digits of 4, and 60 + 4 = 64, a power of two.
For n = 5, 59 in binary is 111011, which has sum of digits of 5, and 59 + 5 = 64.

Maple

a:= n-> 2^(n+add(i, i=Bits[Split](n-1)))-n:
seq(a(n), n=1..32);  # Alois P. Heinz, Jul 05 2024

Prog

(Python)
def a(n):
  return (1 << (n + (n-1).bit_count())) - n

Crossrefs

Cf. A000079, A000120, A092391, A129195, A230300.

Sequence in context: A367663 A330283 A361244 * A262238 A111366 A177127

Adjacent sequences: A374345 A374346 A374347 * A374349 A374352 A374353

Keyword

nonn,base,easy,new

Author

Steven Reyes, Jul 05 2024

Status

approved