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A365884
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Numbers k such that k and k+1 are both terms of A365883.
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4
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27, 188, 459, 620, 675, 836, 1107, 1268, 1323, 1484, 1755, 1916, 1971, 2132, 2403, 2564, 2619, 2780, 3051, 3124, 3212, 3267, 3428, 3699, 3860, 3915, 4076, 4347, 4508, 4563, 4724, 4995, 5156, 5211, 5372, 5643, 5804, 5859, 6020, 6291, 6452, 6507, 6668, 6939, 7100
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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 1, 6, 63, 623, 6216, 62157, 621565, 6215645, 62156450, 621564494, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00621564... .
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LINKS
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EXAMPLE
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27 = 3^3 is a term since its least prime factor, 3, is equal to its exponent, and also the least prime factor of 28 = 2^2 * 7, 2, is equal to its exponent.
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MATHEMATICA
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q[n_] := Equal @@ FactorInteger[n][[1]]; consec[kmax_] := Module[{m = 1, c = Table[False, {2}], s = {}}, Do[c = Join[Rest[c], {q[k]}]; If[And @@ c, AppendTo[s, k - 1]], {k, 1, kmax}]; s]; consec[7200]
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PROG
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(PARI) lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = #Set(factor(k)[1, ]) == 1; if(q1 && q2, print1(k-1, ", ")); q1 = q2); }
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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