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A224490 Smallest k such that k*2*p(n)^2-1=q is prime and k*2*q^2-1 is also prime.

%I A224490 #26 Jan 16 2025 11:51:25
%S A224490 1,1,25,9,21,3,1,16,25,136,10,33,90,250,10,55,1,9,36,75,1,4,33,406,
%T A224490 103,15,121,4,244,78,28,19,49,105,45,34,10,46,33,4,111,15,9,36,118,66,
%U A224490 10,13,31,76,66,36,55,15,4,48,6,66,13,34,54,64,153,1,60,48
%N A224490 Smallest k such that k*2*p(n)^2-1=q is prime and k*2*q^2-1 is also prime.
%H A224490 Pierre CAMI, <a href="/A224490/b224490.txt">Table of n, a(n) for n = 1..10000</a>
%e A224490 1*2*2^2-1=7 prime q 1*2*7^2-1=97 also prime so a(1)=1.
%t A224490 a[n_] := For[k = 1, True, k++, p = Prime[n]; If[PrimeQ[q = k*2*p^2 - 1] && PrimeQ[k*2*q^2 - 1], Return[k]]]; Table[a[n], {n, 1, 66}] (* _Jean-François Alcover_, Apr 12 2013 *)
%o A224490 (PFGW & SCRIPT)
%o A224490 SCRIPT
%o A224490 DIM k
%o A224490 DIM i,0
%o A224490 DIM q
%o A224490 DIMS t
%o A224490 OPENFILEOUT myf,a(n).txt
%o A224490 LABEL a
%o A224490 SET i,i+1
%o A224490 IF i>20000 THEN END
%o A224490 SET k,0
%o A224490 LABEL b
%o A224490 SET k,k+1
%o A224490 SETS t,%d,%d,%d\,;k;i;p(i)
%o A224490 SET q,k*2*p(i)^2-1
%o A224490 PRP q,t
%o A224490 IF ISPRP THEN GOTO c
%o A224490 GOTO b
%o A224490 LABEL c
%o A224490 SET q,k*2*q^2-1
%o A224490 PRP q,t
%o A224490 IF ISPRP THEN WRITE myf,t
%o A224490 IF ISPRP THEN GOTO a
%o A224490 GOTO b
%Y A224490 Cf. A224489, A224491, A224492.
%K A224490 nonn
%O A224490 1,3
%A A224490 _Pierre CAMI_, Apr 08 2013
%E A224490 Typo in name fixed by _Zak Seidov_, Apr 11 2013