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A342187
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Numbers k such that both k and k+1 are not exponentially odd numbers.
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3
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44, 48, 49, 63, 75, 80, 98, 99, 116, 147, 171, 175, 207, 244, 260, 275, 288, 315, 324, 332, 360, 363, 368, 387, 404, 475, 476, 495, 507, 524, 528, 531, 539, 548, 549, 575, 603, 604, 624, 636, 656, 675, 692, 724, 725, 747, 764, 774, 800, 819, 832, 844, 845, 846
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OFFSET
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1,1
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COMMENTS
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The numbers of terms not exceeding 10^k for k = 2, 3, ..., are 8, 64, 624, 6281, 62779, 627904, 6279725, 62796307, 627961560, ... Apparently this sequence has an asymptotic density 0.062796...
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LINKS
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EXAMPLE
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44 is a term since 44 = 2^2 * 11 and 45 = 3^2 * 5 both have an even exponent in their prime factorization.
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MATHEMATICA
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expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; Select[Range[10^3], !expOddQ[#] && !expOddQ[# + 1] &]
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CROSSREFS
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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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