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A060833 Separate the natural numbers into disjoint sets A, B with 1 in A, such that the sum of any 2 distinct elements of the same set never equals 2^k + 2. Sequence gives elements of set A. 5
1, 4, 7, 8, 12, 13, 15, 16, 20, 23, 24, 25, 28, 29, 31, 32, 36, 39, 40, 44, 45, 47, 48, 49, 52, 55, 56, 57, 60, 61, 63, 64, 68, 71, 72, 76, 77, 79, 80, 84, 87, 88, 89, 92, 93, 95, 96, 97, 100, 103, 104, 108, 109, 111, 112, 113, 116, 119, 120, 121, 124, 125, 127, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Can be constructed as follows: place of terms of (2^k+1,2^k+2,...,2^k) are the reflection from (2,3,4,...,2^k,1). [Comment not clear to me - N. J. A. Sloane]

If n == 0 mod 4, then n is in the sequence.  If n == 2 mod 4, then n is not in the sequence.  The number 2n - 1 is in the sequence if and only if n is in the sequence. For n > 1, n is in the sequence if and only if A038189(n-1) = 1. - N. Sato, Feb 12 2013

The set B contains all numbers 2^(k-1)+1 = (2^k+2)/2 (half of the "forbidden sums"), (2, 3, 5, 9, 17, 33, 65,...) = 1/2 * (4, 6, 10, 18, 34, 66, 130, 258,...). - M. F. Hasler, Feb 12 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(1) = 1; and for n > 1: a(n) = A091067(n-1)+1. - Antti Karttunen, Feb 20 2015, based on N. Sato's Feb 12 2013 comment above.

MAPLE

a:= proc(n) option remember; local k, t;

      if n=1 then 1

    else for k from 1+a(n-1) do t:= k-1;

           while irem(t, 2, 'r')=0 do t:=r od;

           if irem(t, 4)=3 then return k fi

         od

      fi

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Feb 12 2013

MATHEMATICA

a[n_] := a[n] = Module[{k, t, q, r}, If[n == 1, 1, For[k = 1+a[n-1], True, k++, t = k-1; While[{q, r} = QuotientRemainder[t, 2]; r == 0, t = q]; If[Mod[t, 4] == 3, Return[k]]]]]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Jan 30 2017, after Alois P. Heinz *)

CROSSREFS

Essentially one more than A091067.

First differences: A106836.

A082410(a(n)) = 0.

Sequence in context: A270941 A270082 A189223 * A162967 A070286 A324978

Adjacent sequences:  A060830 A060831 A060832 * A060834 A060835 A060836

KEYWORD

easy,nonn

AUTHOR

Sen-Peng Eu, May 01 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), May 10 2001

STATUS

approved

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Last modified May 19 11:22 EDT 2019. Contains 323391 sequences. (Running on oeis4.)