A274524 - OEIS

A274524

Numbers n such that both ror(n) and rol(n) are squares, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left.

1, 2, 8, 32, 128, 512, 1568, 2048, 2312, 2592, 2888, 8192, 16928, 32768, 131072, 139392, 250632, 524288, 549152, 566048, 672800, 924800, 963272, 1318688, 2097152, 8388608, 8520192, 8769672, 9005768, 12261152, 13582472, 15635232, 33554432, 134217728, 136059008, 136587392

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OFFSET

1,2

COMMENTS

A004171 and A081294 are subsequences.

From Robert Israel, Jul 13 2016: (Start)

All terms except 1 are even.

Even terms are the numbers of the form n = (a+b)^2/8 such that for some d >= 1,

2^d <= n < 2^(d+1) and 2^(d+1)-1 = a*b. (End)

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

F:= proc(d) local v, R, X;

v:= 2^(d+1)-1;

R:= select(t-> t^2 < v, numtheory:-divisors(v));

op(select(t -> t >= (v+1)/2 and t < v+1, map(t -> (t+ v/t)^2/8, R)));

end proc:

sort(convert({1, seq(F(i), i=1..50)}, list)); # Robert Israel, Jul 13 2016

MATHEMATICA

Select[Range[10^6], Times @ Boole@ {IntegerQ@ Sqrt@ FromDigits[RotateRight@ #, 2], IntegerQ@ Sqrt@ FromDigits[RotateLeft@ #, 2]} &@ IntegerDigits[#, 2] == 1 &] (* Michael De Vlieger, Jun 29 2016 *)

CROSSREFS

Cf. A006257, A038572, A004171, A081294.

Sequence in context: A324568 A320654 A333579 * A081294 A004171 A009117

Adjacent sequences: A274521 A274522 A274523 * A274525 A274526 A274527

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Jun 27 2016

STATUS

approved