



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
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OFFSET

1,1


COMMENTS

a(n) = position of nth 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 nth even term in A026147, and A026147(n) = position of nth 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 kth 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*nhammingweight(n1)%2 \\ Charles R Greathouse IV, Mar 22 2013
(PARI) {a(n) = if( n<1, 0, 2*n  subst( Pol( binary( n1)), x, 1)%2)} /* Michael Somos, Jun 09 2013 */


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



