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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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]

LINKS

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

EXAMPLE

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.

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

PROG

(PFGW & SCRIPT)

SCRIPT

DIM i

DIM j

DIM k

DIM n, 0

DIMS t

OPENFILEOUT myf, a(n).txt

LABEL loop1

SET n, n+1

SETS t, %d, %d\,; n; p(n)

PRP 2*p(n)^2-1, t

IF ISPRP THEN GOTO a

GOTO loop1

LABEL a

SET i, 2*p(n)^2-1

PRP 2*i^2-1, t

IF ISPRP THEN GOTO b

GOTO loop1

LABEL b

SET j, 2*i^2-1

PRP 2*j^2-1, t

IF ISPRP THEN GOTO c

GOTO loop1

LABEL c

WRITE myf, t

SET k, 2*j^2-1

PRP 2*k^2-1

IF ISPRP THEN GOTO d

GOTO loop1

LABEL d

WRITE myf, t

GOTO loop1

(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

CROSSREFS

Cf. A106483.

Sequence in context: A254740 A131263 A235173 * A321055 A185886 A235827

Adjacent sequences:  A245656 A245657 A245658 * A245660 A245661 A245662

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jul 28 2014

EXTENSIONS

More terms from Derek Orr, Jul 28 2014

STATUS

approved

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)