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A057689
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Maximal term in trajectory of P under the 'Px+1' map, where P = n-th prime, or -1 if no such term exists.
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10
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16, 66, 50, 672, 20372, 494, 36918, 1404, 12210, 4248, 5070, 1682, 1850, 2210, 35882, 102720, 94484303672, 30084, 178992, 5330, 246560, 6890, 294253314, 8416400, 515202, 134004, 2810784, 2810883506682183650, 377198408, 320168
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OFFSET
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2,1
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COMMENTS
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LINKS
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EXAMPLE
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For n=3, P=7: trajectory of 7 is 7, 50, 25, 5, 1, 8, 4, 2, 1, 8, 4, 2, 1, 8, 4, 2, 1, ..., which has maximal term 50, cycle length 4 and there are 4 terms before it enters the cycle.
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MATHEMATICA
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Px1[p_, n_]:=Catch[For[i=1, i<PrimePi[p], i++, If[Divisible[n, Prime[i]], Throw[n/Prime[i]]]]; p*n+1];
With[{nmax=50}, Table[Max[NestWhileList[Px1[Prime[n], #]&, Prime[n], UnsameQ, All]], {n, 2, nmax}]] (* Paolo Xausa, Dec 11 2023 *)
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PROG
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(Python)
from sympy import prime, primerange
def a(n):
P = prime(n)
x, plst, seen = P, list(primerange(2, P)), set()
while x > 1 and x not in seen:
seen.add(x)
x = next((x//p for p in plst if x%p == 0), P*x+1)
return max(seen)
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CROSSREFS
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Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057684, A057685, A057686, A057687, A057690, A057691.
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000
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STATUS
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approved
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