

A057691


Number of terms before entering cycle in trajectory of P under the 'Px+1' map, where P = nth 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
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OFFSET

2,1


COMMENTS



LINKS



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)


CROSSREFS

Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057684, A057685, A057686, A057687, A057689, A057690.


KEYWORD

nonn,nice,easy


AUTHOR



EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000


STATUS

approved



