A032911 Numbers whose set of base-4 digits is a subset of {1,3}.

1, 3, 5, 7, 13, 15, 21, 23, 29, 31, 53, 55, 61, 63, 85, 87, 93, 95, 117, 119, 125, 127, 213, 215, 221, 223, 245, 247, 253, 255, 341, 343, 349, 351, 373, 375, 381, 383, 469, 471, 477, 479, 501, 503, 509, 511, 853, 855, 861, 863, 885, 887, 893, 895, 981, 983

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

Numbers that have ones in all even bit positions, counted from least significant bit as position 0. - Ralf Stephan, Nov 01 2003

Examples

			Sequence in binary: 1 11 101 111 1101 1111 10101 10111 11101 11111 ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007090.

Programs

C

#include 
uint32_t a_next(uint32_t a_n) { return (a_n + 1) | (a_n & 0x55555555); } /* Falk Hüffner, Jan 24 2022 */

Magma

[n: n in [1..1000] | Set(IntegerToSequence(n, 4)) subset {1, 3}]; // Vincenzo Librandi, May 31 2012

Mathematica

Flatten[Table[FromDigits[#,4]&/@Tuples[{1,3},n],{n,5}]] (* Vincenzo Librandi, May 31 2012 *)

Python

def A032911(n): return (int(bin(m:=n+1)[3:],4)<<1) + ((1<<(m.bit_length()-1<<1))-1)//3 # Chai Wah Wu, Oct 13 2023

Formula

a(2n) = 4a(n) + 1, a(2n+1) = 4a(n) + 3. - Ralf Stephan, Nov 01 2003