A144794 A positive integer n is included if every 0 in binary n is next to at least one other 0.

4, 8, 9, 12, 16, 17, 19, 24, 25, 28, 32, 33, 35, 36, 39, 48, 49, 51, 56, 57, 60, 64, 65, 67, 68, 71, 72, 73, 76, 79, 96, 97, 99, 100, 103, 112, 113, 115, 120, 121, 124, 128, 129, 131, 132, 135, 136, 137, 140, 143, 144, 145, 147, 152, 153, 156, 159, 192, 193, 195, 196

Offset: 1

Author

Leroy Quet, Sep 21 2008

Keywords

• base
• nonn

Comments

n is included if A144789(n) >= 2.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A144789, A144795.

Programs

Maple

A007814 := proc(n) local nshf,a ; a := 0 ; nshf := n ; while nshf mod 2 = 0 do nshf := nshf/2 ; a := a+1 ; od: a ; end: A144789 := proc(n) option remember ; local lp2,lp2sh,bind ; bind := convert(n,base,2) ; if add(i,i=bind) = nops(bind) then RETURN(0) ; fi; lp2 := A007814(n) ; if lp2 = 0 then A144789(floor(n/2)) ; else lp2sh := A144789(n/2^lp2) ; if lp2sh = 0 then lp2 ; else min(lp2,lp2sh) ; fi; fi; end: isA144794 := proc(n) RETURN(A144789(n) >= 2) ; end: for n from 3 to 400 do if isA144794(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Sep 29 2008

Mathematica

Select[Range@ 200, And[Union@ # != {1}, AllTrue[Map[Length, Select[Split@ #, First@ # == 0 &]], # > 1 &]] &@ IntegerDigits[#, 2] &] (* Michael De Vlieger, Aug 20 2017 *)

Extensions

Extended by R. J. Mathar, Sep 29 2008