A175384 A positive integer k is included if the largest square dividing k is not equal to the largest square that, when written in binary, occurs as a substring in binary k.

17, 19, 27, 33, 34, 35, 37, 38, 39, 41, 45, 51, 54, 57, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 89, 90, 97, 99, 101, 102, 103, 105, 108, 113, 114, 115, 117, 125, 126, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 141, 142, 143, 145, 146

Offset

1,1

Comments

A008833(a(n)) does not equal A162400(a(n)).

Links

Table of n, a(n) for n=1..60.

Example

The largest square dividing 17 is 1. However, 17 in binary is 10001; and the largest square occurring, in its binary representation, within 10001 is 4 (100 in binary). Since 1 does not equal 4, then 17 is in this sequence.

Maple

From R. J. Mathar, Aug 31 2010: (Start)
A008833 := proc(n) local b; b := floor(sqrt(n)) ; while b >= 1 do if n mod (b^2) = 0 then return b^2 ; end if; b := b-1 ; end do: end proc:
A162400 := proc(n) local b, nbin, a; a := 1 ; nbin := convert(n, base, 2) ; for b from 1 to floor(sqrt(n)) do convert(b^2, base, 2) ; if verify(%, nbin, 'sublist') then a := b^2 ; end if; end do: a ; end proc:
isA162400 := proc(n) A008833(n) <> A162400(n) ; end proc:
for n from 1 to 300 do if isA162400(n) then printf("%d, ", n) ; end if; end do: (End)

Crossrefs

Cf. A008833, A162400.

Sequence in context: A073247 A133347 A096990 * A053689 A176462 A060254

Adjacent sequences: A175381 A175382 A175383 * A175385 A175386 A175387

Keyword

base,nonn

Author

Leroy Quet, Apr 24 2010

Extensions

More terms from R. J. Mathar, Aug 31 2010

Status

approved