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%I #25 Mar 03 2023 20:24:01
%S 2,3,5,8,9,12,14,15,17,20,22,23,26,27,29,32,33,36,38,39,42,43,45,48,
%T 50,51,53,56,57,60,62,63,65,68,70,71,74,75,77,80,82,83,85,88,89,92,94,
%U 95,98,99,101,104,105,108,110,111,113,116,118,119,122,123,125,128,129,132
%N Odious numbers (A000069) plus one; complement of A026147.
%C a(n) = position of n-th 2 in A001285 if offset for A001285 is given as 1.
%C 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).
%C 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
%H G. C. Greubel, <a href="/A181155/b181155.txt">Table of n, a(n) for n = 1..1000</a>
%H Edward J. Barbeau, <a href="http://www.maa.org/press/maa-reviews/power-play">Power Play</a>, MAA, 1997. See p. 104.
%F a(n) = A000069(n) + 1.
%F a(a(n)-1) = 2*a(n)-1. - _Benoit Cloitre_, Oct 07 2010
%F a(n) + A010060(n+1) = 2n + 2 for n >= 0. - _Clark Kimberling_, Oct 06 2014
%e 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
%t a[ n_] := If[ n < 1, 0, 2 n - Mod[ Total[ IntegerDigits[ n - 1, 2]], 2]] (* _Michael Somos_, Jun 09 2013 *)
%o (PARI) a(n)=2*n-hammingweight(n-1)%2 \\ _Charles R Greathouse IV_, Mar 22 2013
%o (PARI) {a(n) = if( n<1, 0, 2*n - subst( Pol( binary( n-1)), x, 1)%2)} /* _Michael Somos_, Jun 09 2013 */
%o (Python)
%o def A181155(n): return 1+((m:=n-1)<<1)+(m.bit_count()&1^1) # _Chai Wah Wu_, Mar 03 2023
%Y Cf. A026147.
%K easy,nonn
%O 1,1
%A _Matthew Vandermast_, Oct 06 2010
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