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.

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

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-François 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 A343081 A219329

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