A087272 a(n) is the largest prime number in 3x+1 trajectory initiated at n.

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

Author

Labos Elemer, Sep 18 2003

Keywords

• nonn

Links

• Rémy Sigrist, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A025586, A055510, A087232.

Programs

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 *)

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

Extensions

Offset corrected by Rémy Sigrist, Oct 08 2018