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A337295
Reversible binary Smith numbers: binary Smith numbers (A278909) whose binary reversal (A030101) is also a binary Smith number.
1
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
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Aug 21 2020
STATUS
approved