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 A159615 The slowest increasing sequence beginning with a(1)=2 such that a(n) and n are both odious or both not odious. 10
 2, 4, 5, 7, 9, 10, 11, 13, 15, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 33, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 99, 101, 103, 105, 107, 109, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Vladimir Shevelev, Several results on sequences which are similar to the positive integers, arXiv:0904.2101 [math.NT], 2009. FORMULA For n>=1, a(n)=min{m>a(n-1): A010060(m)=A010060(n)}. a(2n+1)=2a(n)+1. a(2n)=3n+1+j,if n=2^k+j; a(2n)=(10n-4j)/3,if n=2^k+2^(k-1)+j, where 0<=j<=2^(k-1)-1. EXAMPLE If n=3, then k=1, j=0, therefore a(6)=(10*3-4*0)/3=10. MAPLE read("transforms") ; isA000069 := proc(n) option remember ; RETURN( type(wt(n), 'odd') ) ; end: A159615 := proc(n) option remember; if n = 1 then 2; else for a from procname(n-1)+1 do if isA000069(a) = isA000069(n) then RETURN(a) ; fi; od: fi; end: seq(A159615(n), n=1..120) ; # R. J. Mathar, Aug 17 2009 MATHEMATICA odiousQ[n_] := OddQ[DigitCount[n, 2, 1]]; a[1] = 2; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[FreeQ[Array[a, n-1], k] && odiousQ[n] && odiousQ[k] || !odiousQ[n] && !odiousQ[k], Return[k] ] ]; Array[a, 80] (* Jean-François Alcover, Dec 10 2017 *) CROSSREFS Cf. A000069, A159559, A159560, A004760. Sequence in context: A189629 A063113 A122825 * A026463 A243118 A289240 Adjacent sequences:  A159612 A159613 A159614 * A159616 A159617 A159618 KEYWORD nonn,easy AUTHOR Vladimir Shevelev, Apr 17 2009 EXTENSIONS Edited and extended by R. J. Mathar, Aug 17 2009 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)