A337295 Reversible binary Smith numbers: binary Smith numbers (A278909) whose binary reversal (A030101) is also a binary Smith number.

15, 51, 85, 159, 190, 249, 303, 471, 489, 639, 679, 763, 765, 771, 799, 843, 893, 917, 951, 995, 1010, 1017, 1023, 1167, 1203, 1285, 1467, 1501, 1615, 1630, 1641, 1707, 1742, 1773, 1788, 1929, 1939, 1970, 2015, 2167, 2319, 2367, 2493, 2787, 2931, 2975, 3033, 3055

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

159 is a binary Smith number: 159 = 3 * 53 is in binary representation 10011111 = 11 * 110101, and (1 + 0 + 0 + 1 + 1 + 1 + 1 + 1) = (1 + 1) + (1 + 1 + 0 + 1 + 0 + 1) = 6. The binary reversal of 159 = 10011111_2 is 249 = 11111001_2 which is also a binary Smith number: 249 = 3 * 83 is in binary representation 11111001 = 11 * 1010011, and (1 + 1 + 1 + 1 + 1 + 0 + 0 + 1 = (1 + 1) + (1 + 0 + 1 + 0 + 0 + 1 + 1) = 6. Therefore, 159 is a term.

Mathematica

binSmithQ[n_] := CompositeQ[n] && Plus @@ (Last @#* DigitCount[First@#, 2, 1] & /@ FactorInteger[n]) == DigitCount[n, 2, 1]; rev[n_] := FromDigits[Reverse @ IntegerDigits[n, 2], 2]; Select[Range[3000], binSmithQ[#] && binSmithQ[rev[#]] &]

Crossrefs

The binary version of A104171.

Subsequence of A278909.

A334530 is a subsequence.

Cf. A030101.

Sequence in context: A365473 A075933 A075929 * A334530 A044117 A044498

Adjacent sequences: A337292 A337293 A337294 * A337296 A337297 A337298

Keyword

nonn,base

Author

Amiram Eldar, Aug 21 2020

Status

approved