A159615 The slowest increasing sequence beginning with a(1)=2 such that a(n) and n are both odious or both not odious.

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

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