A244638 In the '3x+1' problem, primes which as starting values set new records for number of steps to reach 1, where a step means either 'divide by two' or 'triple plus one and then divide by two'.

2, 3, 7, 19, 31, 41, 73, 97, 193, 257, 313, 487, 859, 937, 1249, 2539, 3331, 3947, 5351, 5839, 7963, 9257, 12343, 21943, 31687, 45127, 60169, 78791, 115547, 180463, 213881, 234239, 270271, 376603, 875681, 1023871, 1252663, 1564063, 2585279, 4063723, 5649499, 9973919, 11200681, 39824647, 41464303, 73583071, 95592191, 226588897, 1359533387, 2263333321, 3349304527

Offset: 1

Author

Zak Seidov and Robert G. Wilson v, Jul 03 2014

Keywords

• nonn

Links

• Wikipedia, Collatz Conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006877, A006577, A006884.

Programs

Mathematica

f[n_] := Length@ NestWhileList[ If[ OddQ@ #, (3 # + 1)/2, #/2] &, n, # > 1 &]  mx = 0; p = 2; lst = {}; While[p < 10^10/2, a = f@ p; If[a > mx, mx = a; Print[{PrimePi@p, p, a - 1}]; AppendTo[ lst, p]]; p = NextPrime@ p]; lst