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A061656 In base 2 n and n^2 contain the same digits in the same proportion. 12
53, 106, 211, 212, 397, 403, 417, 419, 422, 424, 437, 441, 459, 781, 794, 801, 806, 817, 833, 834, 838, 839, 841, 844, 848, 865, 874, 882, 885, 918, 979, 1481, 1549, 1562, 1565, 1571, 1573, 1585, 1588, 1589, 1602, 1612, 1613, 1634, 1637, 1665, 1666, 1667, 1668 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

53 = 110101_2 and 53^2 = 101011111001_2.

MAPLE

p:= n-> add(x^i, i=convert(n, base, 2)):

a:= proc(n) option remember; local k;

      for k from 1+`if`(n=1, 0, a(n-1))

      while p(k)*2<>p(k^2) do od; k

    end:

seq(a(n), n=1..50);  # Alois P. Heinz, May 10 2015

MATHEMATICA

b2pQ[n_]:=Module[{bn=IntegerDigits[n, 2], b2n=IntegerDigits[n^2, 2], cbn0, cb2n0}, cbn0=Count[bn, 0]; cb2n0=Count[b2n, 0]; cbn0>0&&cb2n0>0 && Count[ bn, 1]/cbn0==Count[b2n, 1]/cb2n0]; Select[Range[1700], b2pQ] (* Harvey P. Dale, Jan 25 2012 *)

CROSSREFS

Cf. A061657, A061658, A061659, A061660, A061661, A061662, A061663, A114258, A061664.

Sequence in context: A044523 A063363 A039476 * A141965 A141975 A142663

Adjacent sequences:  A061653 A061654 A061655 * A061657 A061658 A061659

KEYWORD

base,easy,nonn

AUTHOR

Erich Friedman, Jun 16 2001

EXTENSIONS

Offset changed to 1 by Alois P. Heinz, May 10 2015

STATUS

approved

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Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.