A162400 -id:A162400 - cp's OEIS frontend

A162401 a(n) is the largest integer whose square, when represented in binary, is a substring within the binary representation of n.

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 4, 2, 3, 3, 2, 1, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 4, 4, 2, 2, 6, 3, 3, 3, 2, 3, 1, 1, 2, 1, 1, 1, 4, 7, 5, 5, 2, 1, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 8, 4, 4, 4, 2, 2, 2, 2, 6, 6, 3, 3, 3, 3, 3, 3, 4, 9, 3, 3, 2, 1, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 4, 4, 7, 7

Offset: 1

Leroy Quet, Jul 02 2009

A162400(n) = A162401(n)^2.

Alois P. Heinz, Table of n, a(n) for n = 1..16384 (first 10000 terms from Robert G. Wilson v)

Cf. A162400.

f[n_] := Block[{k = Floor@ Sqrt@ n, s = ToString@ FromDigits@ IntegerDigits[n, 2]}, While[ StringPosition[s, ToString@ FromDigits@ IntegerDigits[k^2, 2]] == {}, k-- ]; k]; Array[f, 105] (* Robert G. Wilson v, Jul 16 2009 *)

a(16) correction and more terms from Robert G. Wilson v, Jul 16 2009

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.

Original entry on oeis.org

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

Leroy Quet, Apr 24 2010

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

			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.

Cf. A008833, A162400.

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)

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

cp's OEIS Frontend

A162401 a(n) is the largest integer whose square, when represented in binary, is a substring within the binary representation of n.

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