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URL: https://oeis.org/A224496

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A224496
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.
4
386, 2769, 96656, 5366, 420, 34454, 65039, 192215, 458367, 24735, 27155, 777, 736254, 80297, 279927, 113429, 650474, 238919, 8229, 1284345, 642789, 333141, 11510, 1009271, 932, 395126, 1202174, 25811, 204534, 16286, 22094, 2661131, 22530, 128225, 56225, 900
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, 36}] (* Jean-François Alcover, Apr 12 2013 *)
PROG
(PFGW)
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
KEYWORD
nonn
AUTHOR
Pierre CAMI, Apr 08 2013
STATUS
approved