A026147 a(n) = position of n-th 1 in A001285 or A010059 (Thue-Morse sequence).

1, 4, 6, 7, 10, 11, 13, 16, 18, 19, 21, 24, 25, 28, 30, 31, 34, 35, 37, 40, 41, 44, 46, 47, 49, 52, 54, 55, 58, 59, 61, 64, 66, 67, 69, 72, 73, 76, 78, 79, 81, 84, 86, 87, 90, 91, 93, 96, 97, 100, 102, 103, 106, 107, 109, 112, 114, 115, 117, 120, 121, 124, 126, 127, 130

Offset

1,2

Comments

Barbeau notes that if we let A = the first 2^k terms of this sequence and B = the first 2^k terms of A181155, then the two sets A and B 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

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = 1+A001969(n).

a(n) = Sum_{k=0..2n} mod(-2 + Sum_{j=0..k} floor(C(k, j)/2)}, 3). - Paul Barry, Dec 24 2004

a(n) + A010059(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] - 1] (* Michael Somos, Jun 09 2013 *)

Prog

(PARI) a(n)=2*n+hammingweight(n-1)%2-1 \\ Charles R Greathouse IV, Mar 22 2013
(PARI) {a(n) = if( n<1, 0, 2*n + subst( Pol( binary( n-1)), x, 1)%2 - 1)} /* Michael Somos, Jun 09 2013 */
(Python)
def A026147(n): return 1+((m:=n-1).bit_count()&1)+(m<<1) # Chai Wah Wu, Mar 03 2023

Crossrefs

Cf. A001969, A181155.

Sequence in context: A286491 A133483 A153082 * A032785 A096887 A340161

Adjacent sequences: A026144 A026145 A026146 * A026148 A026149 A026150

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved