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A224492 Smallest k such that k*2*p(n)^2-1=q is prime, k*2*q^2-1=r, k*2*r^2-1=s, k*2*r^2-1=t, r, s, and t are also prime. 9
5103, 36189, 7315, 29608, 128115, 3496, 64590, 143079, 83919, 5586, 13209, 2833, 235339, 61621, 164349, 2668, 84574, 1140, 47335, 108079, 7978, 181366, 146140, 2616, 165864, 86100, 11455, 8925, 23191, 197938, 28194, 229309, 196236, 274186 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

conjecture: a(n) exist for all n

t=k*2*(k*2*(k*2*(k*2*p(n)^2-1)^2-1)^2-1)^2-1

s=k*2*(k*2*(k*2*p(n)^2-1)^2-1)^2-1

r=k*2*(k*2*p(n)^2-1)^2-1

q=k*2*p(n)^2-1

LINKS

Pierre CAMI, Table of n, a(n) for n = 1..80

MATHEMATICA

a[n_] := For[k = 1, True, k++, p = Prime[n]; If[PrimeQ[q = k*2*p^2 - 1] && PrimeQ[r = k*2*q^2 - 1] && PrimeQ[s = k*2*r^2 - 1] && PrimeQ[k*2*s^2 - 1], Return[k]]]; Table[Print[an = a[n]]; an, {n, 1, 34}] (* Jean-Fran├žois Alcover, Apr 12 2013 *)

PROG

(PFGW & SCRIPTIFY)

SCRIPT

DIM k

DIM i, 0

DIM q

DIMS t

OPENFILEOUT myf, a(n).txt

LABEL a

SET i, i+1

IF i>34 THEN END

SET k, 0

LABEL b

SET k, k+1

SETS t, %d, %d, %d\,; k; i; p(i)

SET q, k*2*p(i)^2-1

PRP q, t

IF ISPRP THEN GOTO c

GOTO b

LABEL c

SET q, k*2*q^2-1

PRP q, t

IF ISPRP THEN GOTO d

GOTO b

LABEL d

SET q, k*2*q^2-1

PRP q, t

IF ISPRP THEN GOTO e

GOTO b

LABEL e

SET q, k*2*q^2-1

PRP q, t

IF ISPRP THEN WRITE myf, t

IF ISPRP THEN GOTO a

GOTO b

CROSSREFS

Cf. A224489, A224490, A224491.

Sequence in context: A252143 A223400 A135842 * A330730 A219329 A025398

Adjacent sequences:  A224489 A224490 A224491 * A224493 A224494 A224495

KEYWORD

nonn

AUTHOR

Pierre CAMI, Apr 08 2013

EXTENSIONS

Typo in name fixed by Zak Seidov, Apr 11 2013

STATUS

approved

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Last modified February 23 15:00 EST 2020. Contains 332166 sequences. (Running on oeis4.)