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A057446
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To get next term, multiply by 13, add 1 and discard any prime factors < 13.
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14
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73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101
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OFFSET
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0,1
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COMMENTS
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This is the '13x+1' map. The 'Px+1 map': if x is divisible by any prime < P then divide out these primes one at a time starting with the smallest; otherwise multiply x by P and add 1.
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LINKS
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EXAMPLE
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73 -> 13*73+1 = 950 = 2*5^2*19 -> 19, so second term is 19.
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MATHEMATICA
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m13[n_]:=First[Times@@@Select[FactorInteger[13 n+1], #[[1]]>11&]]; NestList[ m13, 73, 80] (* or *) PadRight[{}, 80, {73, 19, 31, 101}] (* Harvey P. Dale, Apr 16 2019 *)
a[n_] := a[n] = Which[n == 0, 73, n <= 4, Times @@ Power @@@ Select[ FactorInteger[13 a[n - 1] + 1], #[[1]] >= 13&], True, a[n - 4]];
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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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Murad A. AlDamen (Divisibility(AT)yahoo.com), Oct 17 2000
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STATUS
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approved
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