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, 36}] (* Jean-François Alcover, Apr 12 2013 *)
PROG
(PFGW and 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
STATUS
approved