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A372587
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Numbers k such that (sum of binary indices of k) + (sum of prime indices of k) is even.
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7
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6, 7, 10, 11, 13, 14, 18, 19, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 44, 49, 50, 52, 56, 57, 58, 62, 69, 70, 72, 74, 75, 76, 77, 82, 83, 85, 86, 87, 88, 90, 92, 96, 98, 100, 102, 103, 104, 106, 107, 108, 109, 112, 117, 120, 123
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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.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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FORMULA
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EXAMPLE
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The terms (center), their binary indices (left), and their weakly decreasing prime indices (right) begin:
{2,3} 6 (2,1)
{1,2,3} 7 (4)
{2,4} 10 (3,1)
{1,2,4} 11 (5)
{1,3,4} 13 (6)
{2,3,4} 14 (4,1)
{2,5} 18 (2,2,1)
{1,2,5} 19 (8)
{2,3,5} 22 (5,1)
{1,2,3,5} 23 (9)
{4,5} 24 (2,1,1,1)
{1,4,5} 25 (3,3)
{2,4,5} 26 (6,1)
{1,2,4,5} 27 (2,2,2)
{3,4,5} 28 (4,1,1)
{2,3,4,5} 30 (3,2,1)
{1,2,3,4,5} 31 (11)
{1,6} 33 (5,2)
{2,6} 34 (7,1)
{1,2,6} 35 (4,3)
{1,3,6} 37 (12)
{2,3,6} 38 (8,1)
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[100], EvenQ[Total[bix[#]]+Total[prix[#]]]&]
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CROSSREFS
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For just binary indices:
For just prime indices:
A070939 gives length of binary expansion.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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