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A371454
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Numbers whose binary indices are all semiprimes.
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2
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8, 32, 40, 256, 264, 288, 296, 512, 520, 544, 552, 768, 776, 800, 808, 8192, 8200, 8224, 8232, 8448, 8456, 8480, 8488, 8704, 8712, 8736, 8744, 8960, 8968, 8992, 9000, 16384, 16392, 16416, 16424, 16640, 16648, 16672, 16680, 16896, 16904, 16928, 16936, 17152
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OFFSET
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1,1
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COMMENTS
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A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
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LINKS
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EXAMPLE
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The terms together with their binary expansions and binary indices begin:
8: 1000 ~ {4}
32: 100000 ~ {6}
40: 101000 ~ {4,6}
256: 100000000 ~ {9}
264: 100001000 ~ {4,9}
288: 100100000 ~ {6,9}
296: 100101000 ~ {4,6,9}
512: 1000000000 ~ {10}
520: 1000001000 ~ {4,10}
544: 1000100000 ~ {6,10}
552: 1000101000 ~ {4,6,10}
768: 1100000000 ~ {9,10}
776: 1100001000 ~ {4,9,10}
800: 1100100000 ~ {6,9,10}
808: 1100101000 ~ {4,6,9,10}
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MATHEMATICA
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bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
semi[n_]:=PrimeOmega[n]==2;
Select[Range[10000], And@@semi/@bix[#]&]
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CROSSREFS
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Partitions of this type are counted by A101048, squarefree case A002100.
For primes instead of semiprimes we get A326782.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
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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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