A245659 Prime numbers P such that Q=2*P^2-1, R=2*Q^2-1, S=2*R^2-1 and T=2*S^2-1 are all prime numbers.

281683, 496789, 823421, 1352753, 1719217, 6174109, 8643149, 9761051, 9843529, 16191167, 19132121, 19745797, 23490473, 28457797, 31820429, 32860271, 36552277, 37068569, 43506569, 44776981, 46808903, 55035047, 55957807, 67194403, 75099137, 83092897, 86580421, 89135089

Offset: 1

Author

Pierre CAMI, Jul 28 2014

Keywords

• nonn

Comments

Subsequence of A106483.

For P = 496789, 83092897, 467014643, U=2*T^2-1 is also prime. [Corrected by Jens Kruse Andersen, Aug 21 2014]

Examples

			281683 is prime P.
Q=2*P^2-1 = 158690624977 is prime Q.
R=2*Q^2-1 = 50365428911181712501057 is prime R.
S=2*R^2-1 = 5073352858814597404058971422301788780452234497 is prime S.
T=2*S^2-1 = 51477818460084496601334991724899650493354568309112026195311592373475872924903206720553686017 is prime T.
U=2*T^2-1 is composite.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..140

Crossrefs

Cf. A106483.

Programs

Mathematica

f[n_]:=2n^2-1;Select[Prime[Range[5170000]],PrimeQ[f[#]]&&PrimeQ[ f[f[#]]]&&PrimeQ[ f[f[f[#]]]]&&PrimeQ[f[f[f[f[#]]]]]&] (* Farideh Firoozbakht, Aug 11 2014 *)
Select[Prime[Range[52*10^5]],AllTrue[Rest[FoldList[2#^2-1&,{#,#,#,#,#}]],PrimeQ]&] (* Harvey P. Dale, Jan 13 2023 *)

PARI

f(x)=return(2*x^2-1)
forprime(p=1,10^8,if(ispseudoprime(f(p)) && ispseudoprime(f(f(p))) && ispseudoprime(f(f(f(p)))) && ispseudoprime(f(f(f(f(p))))), print1(p,", "))) \\ Derek Orr, Jul 28 2014

Extensions

More terms from Derek Orr, Jul 28 2014