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 A091067 Numbers a(n) such that odd part of a(n) is of form 4k+3. 27

%I

%S 3,6,7,11,12,14,15,19,22,23,24,27,28,30,31,35,38,39,43,44,46,47,48,51,

%T 54,55,56,59,60,62,63,67,70,71,75,76,78,79,83,86,87,88,91,92,94,95,96,

%U 99,102,103,107,108,110,111,112,115,118,119,120,123,124,126,127,131

%N Numbers a(n) such that odd part of a(n) is of form 4k+3.

%C Either of form 2*a(m) or 4k+3, k>=0, 0<m<n.

%C A000265(a(n)) is an element of A004767.

%C a(n) such that A038189(a(n)) = 1.

%C Numbers n such that kronecker(-n, m) = kronecker(m, n) for all m. - _Michael Somos_, Sep 22 2005

%C From _Antti Karttunen_, Feb 20-21 2015: (Start)

%C Gives all n for which A005811(n)-A005811(n-1) = -1, from which follows that a(n) = the least k such that A255070(k) = n.

%C Gives the positions of even terms in A003602.

%C (End)

%C Indices of negative terms in A164677. - _M. F. Hasler_, Aug 06 2015

%C Indices of the 0s in A014577. - _Gabriele Fici_, Jun 02 2016

%H Reinhard Zumkeller, <a href="/A091067/b091067.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A060833(n+1) - 1. [See _N. Sato_'s Feb 12 2013 comment in A060833.]

%F Other identities. For all n >= 1 it holds that:

%F A014707(a(n) + 1) = 1. - _Reinhard Zumkeller_, Sep 28 2011

%F A055975(a(n)) < 0. - _Reinhard Zumkeller_, Apr 28 2012

%F From _Antti Karttunen_, Feb 20-21 2015: (Start)

%F a(n) = A246590(n)/2.

%F A255070(a(n)) = n, or equally, A236840(a(n)) = 2n.

%F a(n) = 1 + A255068(n-1).

%F (End)

%o (PARI) for(n=1,200,if(((n/2^valuation(n,2)-1)/2)%2,print1(n",")))

%o (PARI) {a(n) = local(m, c); if( n<1, 0, c=0; m=1; while( c<n, m++; if( ((m/2^valuation(m, 2) - 1) / 2) % 2, c++)); m)}; /* _Michael Somos_, Sep 22 2005 */

%o (Haskell)

%o import Data.List (elemIndices)

%o a091067 n = a091067_list !! (n-1)

%o a091067_list = map (+ 1) \$ elemIndices 1 a014707_list

%o -- _Reinhard Zumkeller_, Sep 28 2011

%o (Scheme, with Antti Karttunen's IntSeq-library, two versions)

%o (define A091067 (MATCHING-POS 1 1 (COMPOSE even? A003602)))

%o (define A091067 (NONZERO-POS 1 0 A038189))

%o ;; _Antti Karttunen_, Feb 20 2015

%o (PARI) is_A091067(n)=bittest(n,valuation(n,2)+1) \\ _M. F. Hasler_, Aug 06 2015

%Y Essentially one less than A060833.

%Y Characteristic function: A038189.

%Y Complement of A091072.

%Y First differences are in A106836 (from its second term onward).

%Y Sequence A246590 gives the even terms.

%Y Gives the positions of records (after zero) for A255070 (equally, the position of the first n there).

%Y Cf. A106837 (gives n such that both n and n+1 are terms of this sequence).

%Y Cf. A098502 (gives n such that both n and n+2 are, but n+1 is not in this sequence).

%Y Cf. also A000265, A003602, A004767, A005811, A014707, A055975, A236840, A255068, A255327, A255330.

%K nonn,easy

%O 1,1

%A _Ralf Stephan_, Feb 22 2004

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Last modified May 26 07:44 EDT 2019. Contains 323579 sequences. (Running on oeis4.)