A119435 a(n) = (binary reversal of n)-th integer among those positive integers not occurring earlier in the sequence.

1, 2, 5, 3, 9, 7, 13, 4, 17, 12, 23, 10, 22, 18, 29, 6, 33, 24, 43, 16, 40, 31, 51, 14, 41, 30, 53, 25, 49, 38, 61, 8, 65, 45, 83, 32, 76, 58, 95, 21, 74, 55, 94, 42, 87, 68, 107, 19, 78, 56, 100, 39, 91, 70, 113, 34, 89, 66, 112, 52, 104, 81, 125, 11, 129, 86, 163, 60, 148

Offset: 1

Author

Leroy Quet, May 19 2006

Keywords

• easy
• nonn
• base
• look

Comments

This sequence is a permutation of the positive integers.

[Proof from N. J. A. Sloane, Apr 20 2022: a(n) always exists, so the sequence is infinite. Every time n is a power of 2, n-reversed is 1, and a(n) is the smallest missing number. Since there are infinitely many powers of 2, every number will eventually appear.]

Examples

			12 in binary is 1100; so its binary reversal is 0011, which is 3 in decimal. Those positive integers not among the first 11 terms of the sequence are 6,8,10,11,14,..., and the third of these is 10, so a(12) = 10.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000, first 1000 terms from Diana L. Mecum.
• Michael De Vlieger, Extended Table of n, a(n) for n = 1..2^16.
• Michael De Vlieger, Scatterplot of a(n), n = 1..2^16.
• Michael De Vlieger, Log-log scatterplot of a(n), n = 1..2^16.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A030101, A119436 (inverse).

Programs

Mathematica

Block[{a = {1}, nn = 69}, Do[AppendTo[a, #] &@ Complement[Range[i + 2 nn], #][[FromDigits[#, 2] &@ Reverse@ IntegerDigits[i, 2]]] &@ a, {i, 2, nn}]; a] (* Michael De Vlieger, Sep 03 2017 *)

Extensions

More terms from Diana L. Mecum, Jul 21 2008