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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
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
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
KEYWORD
nonn
AUTHOR
Pierre CAMI, Apr 08 2013
EXTENSIONS
Typo in name fixed by Zak Seidov, Apr 11 2013
STATUS
approved