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A247648 Numbers whose binary expansion begins and ends with 1 and does not contain two adjacent zeros. 11
1, 3, 5, 7, 11, 13, 15, 21, 23, 27, 29, 31, 43, 45, 47, 53, 55, 59, 61, 63, 85, 87, 91, 93, 95, 107, 109, 111, 117, 119, 123, 125, 127, 171, 173, 175, 181, 183, 187, 189, 191, 213, 215, 219, 221, 223, 235, 237, 239, 245, 247, 251, 253 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Decimal equivalents of A247647.

A265716(a(n)) = A265705(2*a(n),a(n)) = 2*a(n). - Reinhard Zumkeller, Dec 15 2015

The viabin numbers of the integer partitions having distinct parts (for the definition of viabin number see comment in A290253). For example, 109 is in the sequence because it is the viabin number of the integer partition [5,4,2]; 121 is not in the sequence because it is the viabin number of the integer partition [5,4,4]. - Emeric Deutsch, Aug 29 2017

LINKS

Chai Wah Wu and Reinhard Zumkeller, Table of n, a(n) for n = 1..121392, all terms < 2^24; first 1000 terms from Chai Wah Wu

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.

EXAMPLE

109 is in the sequence because its binary expansion is 1101101.

MAPLE

vitopart := proc (n) local L, i, j, N, p, t: N := 2*n: L := ListTools:-Reverse(convert(N, base, 2)): j := 0: for i to nops(L) do if L[i] = 0 then j := j+1: p[j] := numboccur(L[1 .. i], 1) end if end do: sort([seq(p[t], t = 1 .. j)], `>=`) end proc: a := proc (n) if n = 1 then 1 elif `mod`(n, 2) = 0 then a((1/2)*n) elif `mod`(n, 2) = 1 and `mod`((1/2)*n-1/2, 2) = 0 then a((1/2)*n-1/2)+1 else a((1/2)*n-1/2) end if end proc: A := {}: for n to 254 do if a(n) = nops(vitopart(n)) then A := `union`(A, {n}) else end if end do: A; # program is based on my comment; the command vitopart(n) yields the integer partition having viabin number n. # Emeric Deutsch, Aug 29 2017

MATHEMATICA

Select[Range@ 256, And[First@ # == Last@ # == 1, NoneTrue[Map[Length, Select[Split[#], First@ # == 0 &]], # > 1 &]] &@ IntegerDigits[#, 2] &] (* Michael De Vlieger, Aug 29 2017 *)

PROG

(Python)

A247648_list = [n for n in range(1, 10**5) if n % 2 and not '00' in bin(n)]

# Chai Wah Wu, Sep 25 2014

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a247648 n = a247648_list !! (n-1)

a247648_list = f $ singleton 1 where

   f s = x : f (insert (4 * x + 1) $ insert (2 * x + 1) s')

         where (x, s') = deleteFindMin s

-- Reinhard Zumkeller, Sep 25 2014

CROSSREFS

Cf. A247647, A247649, A253085.

Cf. A247875 (complement).

Cf. A265716, A265705.

Sequence in context: A292939 A232011 A153183 * A117203 A081118 A003255

Adjacent sequences:  A247645 A247646 A247647 * A247649 A247650 A247651

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Sep 25 2014

STATUS

approved

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Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)