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A057691 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. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
See A057684 for definition.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 2..10001 (terms 2..1000 from T. D. Noe)
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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)
print([a(n) for n in range(2, 82)]) # Michael S. Branicky, Dec 11 2023
CROSSREFS
Sequence in context: A065865 A088618 A121645 * A297903 A298497 A246922
KEYWORD
nonn,nice,easy
AUTHOR
N. J. A. Sloane, Oct 20 2000
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000
STATUS
approved

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Last modified May 21 08:24 EDT 2024. Contains 372729 sequences. (Running on oeis4.)