A337221 Starts of record-length sequences of primes under iteration of the map x goes to (3*x+1)/2.

2, 3, 7, 31, 2111, 89599, 44102911, 35014031359, 42884741301247, 4322284854745087, 571673085017796607, 2374135870748049407

Offset

1,1

Comments

Dickson's conjecture implies this sequence is infinite.

For all n > 2, a(n) mod 10 == 1, 7 or 9. - Chai Wah Wu, Aug 21 2020

Links

Table of n, a(n) for n=1..12.

Example

a(3)=7 is in the sequence because iterating x -> (3*x+1)/2 starting with 7 we get a sequence of three primes 7 -> 11 -> 17, and there is no such sequence of three or more primes starting with a prime less than 7.

Maple

f:= proc(n) local R, x;
  if not isprime(n) then return 0 fi;
  x:= n;
  R:= 1;
  do
    x:= (3*x+1)/2;
    if not (x::integer and isprime(x)) then return R fi;
    R:= R+1;
  od
end proc:
R:= 2: x:= 2: rec:= 1:
while rec < 10 do
  for x from ceil(x/2^rec)*2^rec-1 by 2^rec do
    v:= f(x);
    if v > rec then rec:= v; R:= R, x; break fi
od od:
R;

Mathematica

g[n_] := Length@NestWhileList[(3 # + 1)/2 &, n, PrimeQ] - 1;
r = {2}; x = 2; rec = 1;
While[rec < 10,
  For[x = Ceiling[x/2^rec]*2^rec-1, x<Infinity, x=x+2^rec,
   v = g[x];
If[v > rec, rec = v; AppendTo[r, x]; Break[]]]]; r (* Robert Price, Aug 28 2020, based on Maple program by Robert Israel *)

Crossrefs

Sequence in context: A018239 A096350 A066279 * A161471 A057677 A032148

Adjacent sequences: A337218 A337219 A337220 * A337222 A337223 A337224

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Aug 19 2020

Extensions

a(8) from Chai Wah Wu, Aug 20 2020

a(9) from Chai Wah Wu, Aug 21 2020

a(10) from Bert Dobbelaere, Aug 27 2020

a(11) from Bert Dobbelaere, Aug 29 2020

a(12) from Bert Dobbelaere, Aug 30 2020

Status

approved