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A091072 Numbers whose odd part is of the form 4k+1. The bit to the left of the least significant bit of each term is unset. 23
1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 21, 25, 26, 29, 32, 33, 34, 36, 37, 40, 41, 42, 45, 49, 50, 52, 53, 57, 58, 61, 64, 65, 66, 68, 69, 72, 73, 74, 77, 80, 81, 82, 84, 85, 89, 90, 93, 97, 98, 100, 101, 104, 105, 106, 109, 113, 114, 116, 117, 121, 122, 125, 128, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Either of form 2a(m) or 4k+1, k >= 0, 0 < m < n.
A000265(a(n)) is an element of A016813.
a(n) such that A038189(a(n)) = 0.
Numbers n such that kronecker(n, m) = kronecker(m, n) for all m. - Michael Somos, Sep 24 2005
The Dragon curve A014577 (but changing the offset to 1: (1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ...) = the characteristic function of A091072. - Gary W. Adamson, Apr 11 2010
A014707(a(n) + 1) = 0. - Reinhard Zumkeller, Sep 28 2011
A055975(a(n)) > 0. - Reinhard Zumkeller, Apr 28 2012
Also indices of 1 in A034947. - Jianing Song, Apr 24 2021
The terms in the sequence are the same as the terms in the odd columns of the table in A135764 with headings 4k+1: (1, 5, 9, 13...). A014577(n) = 1 if n is in that set, but A014577(n) = 0 if n is in the set of even columns in the A135764 table. - Gary W. Adamson, May 29 2021
LINKS
J.-P. Allouche and J. Shallit, On three conjectures of P. Barry, arxiv preprint arXiv:2006.04708 [math.NT], June 8 2020.
Kevin Ryde, Iterations of the Dragon Curve, see index TurnLeft, with a(n) = TurnLeft(n-1).
J. E. S. Socolar and J. M. Taylor, An aperiodic hexagonal tile, arXiv:1003.4279 [math.CO], 2010.
EXAMPLE
x + 2*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 9*x^6 + 10*x^7 + 13*x^8 + 16*x^9 + ...
MATHEMATICA
Select[ Range[129], EvenQ[ (#/2^IntegerExponent[#, 2] - 1)/2 ] & ] (* Jean-François Alcover, Feb 16 2012, after Pari *)
PROG
(PARI) for(n=1, 200, if(((n/2^valuation(n, 2)-1)/2)%2==0, print1(n", ")))
(PARI) {a(n) = local(m, c); if( n<1, 0, c=1; m=1; while( c<n, m++; if( ((m / 2^valuation( m, 2) - 1) / 2)%2==0, c++)); m)} /* Michael Somos, Sep 24 2005 */
(PARI) a(n) = if(n=2*n-2, my(t=1); forstep(i=logint(n, 2), 0, -1, if(bittest(n, i)==t, n--; t=!t))); n+1; \\ Kevin Ryde, Mar 21 2021
(Haskell)
import Data.List (elemIndices)
a091072 n = a091072_list !! (n-1)
a091072_list = map (+ 1) $ elemIndices 0 a014707_list
-- Reinhard Zumkeller, Sep 28 2011
CROSSREFS
Complement of A091067.
Cf. A014577 (characteristic function), A034947, A106841 (first of triplet), A088742 (first differences), A339597.
Sequence in context: A084581 A121996 A269176 * A001481 A248151 A245226
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Feb 22 2004
STATUS
approved

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Last modified June 25 18:08 EDT 2024. Contains 373707 sequences. (Running on oeis4.)