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A337295
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Reversible binary Smith numbers: binary Smith numbers (A278909) whose binary reversal (A030101) is also a binary Smith number.
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1
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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[#]] &]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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