A380934 Elias delta encoding of n converted from base 2 to integer.

1, 4, 5, 12, 13, 14, 15, 32, 33, 34, 35, 36, 37, 38, 39, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219

Offset: 1

Author

Darío Clavijo, Apr 21 2025

Keywords

• nonn
• base

Comments

This is the Elias delta coding of n with leading zeros omited.

Examples

			For n = 16 a(16) = 80 because:
16 = 10000_2 and
Strip leading bit of n = 0000_2.
16 is of bitsize 5.
Prepend 5-1 zeros and 5 as 101_2
0000101_2 + 0000_2 = 00001010000_2 = 80.
		

Links

• Wikipedia, Elias delta coding

Crossrefs

Cf. A281150.

Programs

Mathematica

A380934[n_] := FromDigits[Join[IntegerDigits[BitLength[n], 2], Rest[IntegerDigits[n, 2]]], 2] (* James C. McMahon, Apr 30 2025 *)

Python

def a(n):
    if n == 1: return 1
    b = bin(n)[2:]
    L = len(b)
    g = '0' * (L - 1) + bin(L)[2:]
    d = g + b[1:]
    return int(d,2)
print([a(n) for n in range(1,60)])

Python

def A380934(n): return int(bin(n.bit_length())+bin(n)[3:],2) # Chai Wah Wu, Apr 21 2025