A162719 A positive integer n is included if n in binary contains as many 0's as the number of 1's in the binary representation of n+1, and if n in binary contains as many 1's as the number of 0's in the binary representation of n+1.

4, 9, 18, 19, 20, 24, 37, 39, 41, 49, 70, 74, 75, 76, 79, 82, 83, 84, 88, 98, 99, 100, 104, 112, 141, 149, 151, 153, 159, 165, 167, 169, 177, 197, 199, 201, 209, 225, 270, 278, 282, 283, 284, 294, 298, 299, 300, 303, 306, 307, 308, 312, 319, 326, 330, 331, 332

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

39 in binary is 100111, which has two 0's and four 1's. 39+1 = 40 is 101000 in binary, which contains two 1's and four 0's. Since the number of 0's in binary 39 equals the number of 1's in binary 40, and because the number of 1's in binary 39 equals the number of 0's in binary 40, then 39 is in the sequence.

Maple

read("transforms") ; A070939 := proc(n) max(1, ilog2(n)+1) ; end: A023416 := proc(n) A070939(n)-wt(n) ; end: isA162719 := proc(n) RETURN( A023416(n) = wt(n+1) and wt(n) = A023416(n+1)) ; end: for n from 1 to 999 do if isA162719(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Aug 01 2009

Mathematica

Select[Range[400], DigitCount[#, 2, 0]==DigitCount[#+1, 2, 1]&&DigitCount[#, 2, 1]==DigitCount[#+1, 2, 0]&] (* Harvey P. Dale, Nov 02 2024 *)

Crossrefs

Sequence in context: A088365 A139468 A127081 * A352997 A313357 A313358

Adjacent sequences: A162716 A162717 A162718 * A162720 A162721 A162722

Keyword

base,nonn

Author

Leroy Quet, Jul 11 2009

Extensions

Extended beyond a(8) by R. J. Mathar, Aug 01 2009

Status

approved