A181155 Odious numbers (A000069) plus one; complement of A026147.

2, 3, 5, 8, 9, 12, 14, 15, 17, 20, 22, 23, 26, 27, 29, 32, 33, 36, 38, 39, 42, 43, 45, 48, 50, 51, 53, 56, 57, 60, 62, 63, 65, 68, 70, 71, 74, 75, 77, 80, 82, 83, 85, 88, 89, 92, 94, 95, 98, 99, 101, 104, 105, 108, 110, 111, 113, 116, 118, 119, 122, 123, 125, 128, 129, 132

Offset

1,1

Comments

a(n) = position of n-th 2 in A001285 if offset for A001285 is given as 1.

It appears that this sequence and A026147 index each other's even terms (i.e., a(n) = position of n-th even term in A026147, and A026147(n) = position of n-th even term in this sequence). It also appears that each of the two sequences indexes its own odd terms (cf. A079000).

Barbeau notes that if let A = the first 2^k terms of A026147 and B = the first 2^k terms of this sequence, then the two sets have the same sum of powers for first up to the k-th power. I note it holds for 0th power also. - Michael Somos, Jun 09 2013

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Edward J. Barbeau, Power Play, MAA, 1997. See p. 104.

Formula

a(n) = A000069(n) + 1.

a(a(n)-1) = 2*a(n)-1. - Benoit Cloitre, Oct 07 2010

a(n) + A010060(n+1) = 2n + 2 for n >= 0. - Clark Kimberling, Oct 06 2014

Example

Let k=2. Then A = {1,4,6,7} and B = {2,3,5,8} have the property that 1^0+4^0+6^0+7^0 = 2^0+3^0+5^0+8^0 = 4, 1^1+4^1+6^1+7^1 = 2^1+3^1+5^1+8^1 = 18, and 1^2+4^2+6^2+7^2 = 2^2+3^2+5^2+8^2 = 102. - Michael Somos, Jun 09 2013

Mathematica

a[ n_] := If[ n < 1, 0, 2 n - Mod[ Total[ IntegerDigits[ n - 1, 2]], 2]] (* Michael Somos, Jun 09 2013 *)

Prog

(PARI) a(n)=2*n-hammingweight(n-1)%2 \\ Charles R Greathouse IV, Mar 22 2013
(PARI) {a(n) = if( n<1, 0, 2*n - subst( Pol( binary( n-1)), x, 1)%2)} /* Michael Somos, Jun 09 2013 */
(Python)
def A181155(n): return 1+((m:=n-1)<<1)+(m.bit_count()&1^1) # Chai Wah Wu, Mar 03 2023

Crossrefs

Cf. A026147.

Sequence in context: A192391 A013634 A133484 * A153081 A190841 A095952

Adjacent sequences: A181152 A181153 A181154 * A181156 A181157 A181158

Keyword

easy,nonn

Author

Matthew Vandermast, Oct 06 2010

Status

approved