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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: A063363 A288619 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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