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a(1) = 1. a(n) = the smallest integer >=2 such that (product{k=1 to n} a(k)) in binary is a palindrome.
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%I #9 Mar 15 2015 20:10:09

%S 1,3,3,3,7,13,5,13,57,223,5419,17,241,4192257,16773121,17,241

%N a(1) = 1. a(n) = the smallest integer >=2 such that (product{k=1 to n} a(k)) in binary is a palindrome.

%C All terms are odd.

%C There are an infinite number of terms.

%C a(18) > 11000000001. - _Robert G. Wilson v_, Jun 30 2009

%F For n>=2, a(n) = A143014(n)/A143014(n-1).

%t f[n_] := f[n] = Block[{k = 3, a = Times @@ Table[ f@i, {i, n - 1}]}, While[ id = IntegerDigits[a*k, 2]; id != Reverse@id, k += 2]; k]; f[1]=1; Array[f, 17] (* _Robert G. Wilson v_, Jun 30 2009 *)

%Y Cf. A143014, A143016.

%K base,more,nonn

%O 1,2

%A _Leroy Quet_, Jul 15 2008

%E a(6)-a(17) from _Ray Chandler_, Jun 21 2009