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
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
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