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A280268
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Numbers k such that Pell(k) and Pell(k+1) have the same prime signature where Pell(k) = A000129(k).
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0
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2, 14, 26, 38, 86, 94, 106, 214, 218, 334, 338, 381, 590, 605
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OFFSET
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1,1
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COMMENTS
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Initial terms are 2, 2*7, 2*13, 2*19, 2*43, 2*47, 2*53, 2*107, 2*109.
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LINKS
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EXAMPLE
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14 is a term because A000129(14) = 2 * 13^2 * 239 and A000129(15) = 5^2 * 29 * 269.
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MATHEMATICA
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psig[n_]:=Sort[FactorInteger[n][[;; , 2]]]; Drop[With[{nn=220}, SequencePosition[psig/@ LinearRecurrence[ {2, 1}, {0, 1}, nn], {x_, x_}]][[;; , 1]]-1, 2] (* The program generates the first 9 terms of the sequence. *) (* Harvey P. Dale, Jul 07 2024 *)
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PROG
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(PARI) Pell(n) = ([2, 1; 1, 0]^n)[2, 1];
is(n) = vecsort(factor(Pell(n))[, 2]) == vecsort(factor(Pell(n+1))[, 2]);
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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