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

Author

Steven Reyes, Jul 05 2024

Keywords

• nonn
• base
• easy

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

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

Python

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

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).