A203070 -id:A203070 - cp's OEIS frontend

A141709 Least positive multiple of n which is palindromic in base 2, allowing for leading zeros (or: ignoring trailing zeros).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 33, 12, 65, 14, 15, 16, 17, 18, 513, 20, 21, 66, 2047, 24, 325, 130, 27, 28, 1421, 30, 31, 32, 33, 34, 455, 36, 2553, 1026, 195, 40, 1025, 42, 129, 132, 45, 4094, 4841, 48, 1421, 650, 51, 260, 3339, 54, 165, 56, 513, 2842, 6077, 60, 427, 62

Offset: 1

M. F. Hasler, Jul 17 2008

Even numbers cannot be palindromic in base 2, unless leading zeros are considered (or, equivalently, resp. more precisely, trailing zeros are discarded). This is done in this version of A141708, which therefore does not need to be restricted to odd n as it has been done for A141707 and A141708.

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

Cf. A050782, A141707-A141708, A062279, A203070, A000265, A178225.

a141709 n = until ((== 1) . a178225 . a000265) (+ n) n
-- Reinhard Zumkeller, Nov 06 2012

notpalbinQ[i_]:=Module[{id=IntegerDigits[i,2]},While[Last[id]==0,id=Most[id]];id!= Reverse[id]]; lm[n_]:=Module[{k=1},While[notpalbinQ[k n],k++];k n]; Array[lm,70] (* Harvey P. Dale, Dec 28 2011 *)

A141709(n)=forstep(k=n,10^9,n,vecextract(t=binary(k>>valuation(k,2)),"-1..1")-t || return(k))

A178225(A000265(a(n))) = 1. - Reinhard Zumkeller, Nov 06 2012

cp's OEIS Frontend

A141709 Least positive multiple of n which is palindromic in base 2, allowing for leading zeros (or: ignoring trailing zeros).

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