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A372431
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Positive integers k such that the prime indices of k are disjoint from the binary indices of k.
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4
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1, 2, 4, 7, 8, 9, 10, 11, 12, 13, 16, 17, 19, 21, 23, 24, 25, 26, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 53, 57, 58, 59, 61, 62, 64, 65, 67, 69, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 84, 86, 89, 92, 93, 94, 96, 97, 98, 101
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OFFSET
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1,2
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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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EXAMPLE
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The binary indices of 65 are {1,7}, and the prime indices are {3,6}, so 65 is in the sequence.
The terms together with their prime indices begin:
1: {}
2: {1}
4: {1,1}
7: {4}
8: {1,1,1}
9: {2,2}
10: {1,3}
11: {5}
12: {1,1,2}
13: {6}
16: {1,1,1,1}
The terms together with their binary expansions and binary indices begin:
1: 1 ~ {1}
2: 10 ~ {2}
4: 100 ~ {3}
7: 111 ~ {1,2,3}
8: 1000 ~ {4}
9: 1001 ~ {1,4}
10: 1010 ~ {2,4}
11: 1011 ~ {1,2,4}
12: 1100 ~ {3,4}
13: 1101 ~ {1,3,4}
16: 10000 ~ {5}
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MATHEMATICA
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bix[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Intersection[bix[#], prix[#]]=={}&]
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CROSSREFS
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For subset instead of disjoint we have A372430.
A070939 gives length of binary expansion.
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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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