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A057691
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Number of terms before entering cycle in trajectory of P under the 'Px+1' map, where P = n-th prime, or -1 if trajectory does not cycle.
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10
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5, 13, 4, 10, 25, 11, 68, 14, 39, 34, 9, 4, 5, 5, 16, 16, 234, 23, 16, 5, 11, 5, 63, 116, 18, 18, 33, 288, 47, 29, 317, 14, 12, 61, 60, 6, 16, 10, 5, 14, 46, 5, 6, 15, 105, 4, 11, 48, 44, 5, 6, 10, 5, 55, 15, 14, 25, 17, 9, 16, 6, 7, 26, 5, 33, 46, 5, 16, 23, 13, 15, 11, 16, 14, 11
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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];
Module[{nmax=100, m}, Table[FirstPosition[m=NestWhileList[Px1[Prime[n], #]&, Prime[n], UnsameQ, All], Last[m]][[1]]-1, {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, traj, seen = P, list(primerange(2, P)), [], set()
while x not in seen:
traj.append(x)
seen.add(x)
x = next((x//p for p in plst if x%p == 0), P*x+1)
return traj.index(x)
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CROSSREFS
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Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057684, A057685, A057686, A057687, A057689, A057690.
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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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