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A087272
a(n) is the largest prime number in 3x+1 trajectory initiated at n.
7
2, 5, 2, 5, 5, 17, 2, 17, 5, 17, 5, 13, 17, 53, 2, 17, 17, 29, 5, 2, 17, 53, 5, 29, 13, 1619, 17, 29, 53, 1619, 2, 29, 17, 53, 17, 37, 29, 101, 5, 1619, 2, 43, 17, 17, 53, 1619, 5, 37, 29, 29, 13, 53, 1619, 1619, 17, 43, 29, 101, 53, 61, 1619, 1619, 2, 37, 29, 101, 17, 13, 53
OFFSET
2,1
LINKS
MATHEMATICA
c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1); c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] ofp[x_] := Part[fpl[x], Flatten[Position[PrimeQ[fpl[x]], True]]] Table[Max[ofp[w]], {w, 1, 256}]
Table[Max[Select[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&], PrimeQ]], {n, 2, 70}] (* Harvey P. Dale, Feb 27 2023 *)
PROG
(PARI) a(n) = my (mx=2); while (n>1, if (isprime(n), mx=max(mx, n)); n=if (n%2, 3*n+1, n/2)); mx \\ Rémy Sigrist, Oct 08 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 18 2003
EXTENSIONS
Offset corrected by Rémy Sigrist, Oct 08 2018
STATUS
approved