OFFSET
1,1
COMMENTS
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
KEYWORD
easy,nonn
AUTHOR
Matthew Vandermast, Oct 06 2010
STATUS
approved