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A057216
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To get next term, multiply by 17, add 1 and discard any prime factors < 17.
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14
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61, 173, 1471, 521, 4429, 4183, 2963, 257, 437, 743, 1579, 2237, 3803, 2309, 19627, 5561, 47269, 14881, 3833, 32581, 263, 43, 61, 173, 1471, 521, 4429, 4183, 2963, 257, 437, 743, 1579, 2237, 3803, 2309, 19627, 5561, 47269, 14881, 3833, 32581, 263, 43
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OFFSET
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0,1
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COMMENTS
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This is the '17x+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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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
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EXAMPLE
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61 -> 17*61+1 = 1038 = 2*3*173 -> 173, so second term is 173.
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MATHEMATICA
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a[n_] := a[n] = Which[n == 0, 61, n <= 22, Times @@ Power @@@ Select[ FactorInteger[17 a[n - 1] + 1], #[[1]] >= 17&], True, a[n - 22]];
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PROG
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(PARI) lista(nn) = {my(x=61); for (n=1, nn, print1(x, ", "); my(f=factor(17*x+1)); for (k=1, #f~, if (f[k, 1] < 17, f[k, 1] = 1)); x = factorback(f); ); } \\ Michel Marcus, Jan 19 2021
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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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EXTENSIONS
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More terms from James A. Sellers and Larry Reeves (larryr(AT)acm.org), Oct 18 2000
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STATUS
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approved
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