

A272758


Perfect powers whose binary reversal is also a perfect power.


0



1, 4, 8, 9, 16, 27, 32, 36, 64, 128, 144, 216, 256, 512, 576, 1024, 1728, 2048, 2304, 4096, 8192, 9216, 13824, 16384, 32768, 36864, 65536, 110592, 131072, 147456, 262144, 524288, 589824, 884736, 1048576, 2097152, 2359296, 4194304, 7077888, 8388608, 9437184, 16777216
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OFFSET

1,2


COMMENTS

All powers of 2 (A000079) are terms.  Michel Marcus, May 06 2016


LINKS

Table of n, a(n) for n=1..42.


EXAMPLE

The binary expansion of 16=2^4 is 10000, its reversal is 1, a square, so 16 is a term.


MATHEMATICA

fQ[n_] := n == 1  GCD @@ FactorInteger[n][[All, 2]] > 1; Select[Select[Range[2^20], fQ], fQ@ FromDigits[Reverse@ IntegerDigits[#, 2], 2] &] (* Michael De Vlieger, May 05 2016, after Ant King and Robert G. Wilson v at A001597 *)


PROG

(PARI) isp(n) = (n==1)  ispower(n);
isok(n) = isp(n) && isp(subst(Polrev(binary(n)), x, 2)); \\ Michel Marcus, May 06 2016


CROSSREFS

Cf. A001597, A030101, A118895 (base10 analog).
Sequence in context: A155568 A067252 A324723 * A227645 A285438 A089042
Adjacent sequences: A272755 A272756 A272757 * A272759 A272760 A272761


KEYWORD

nonn,base


AUTHOR

Benjamin Przybocki, May 05 2016


STATUS

approved



