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Smallest k such that k*2*p(n)^2+1 is prime.
3

%I #20 Sep 22 2019 17:04:13

%S 2,1,2,2,3,2,6,15,12,6,8,2,5,6,2,14,3,23,2,5,2,3,5,3,6,11,2,9,3,5,6,3,

%T 14,8,5,6,2,2,5,9,8,11,3,2,11,3,6,5,6,5,2,5,3,8,15,14,3,5,20,5,6,14,

%U 14,8,5,2,8,2,6,18,14,3,6,9,5,12,3,9,15,18,6,6,3

%N Smallest k such that k*2*p(n)^2+1 is prime.

%H Pierre CAMI, <a href="/A224493/b224493.txt">Table of n, a(n) for n = 1..10000</a>

%t a[n_] := For[k = 1, True, k++, p = Prime[n]; If[PrimeQ[k*2*p^2 + 1], Return[k]]]; Table[ a[n] , {n, 1, 83}] (* _Jean-François Alcover_, Apr 12 2013 *)

%t sk[n_]:=Module[{k=1},While[!PrimeQ[2*k*n^2+1],k++];k]; Table[sk[n],{n,Prime[ Range[ 90]]}] (* _Harvey P. Dale_, Sep 22 2019 *)

%o (PFGW & SCRIPTIFY)

%o SCRIPT

%o DIM k

%o DIM i,0

%o DIM q

%o DIMS t

%o OPENFILEOUT myf,a(n).txt

%o LABEL a

%o SET i,i+1

%o IF i>10000 THEN END

%o SET k,0

%o LABEL b

%o SET k,k+1

%o SETS t,%d,%d,%d\,;k;i;p(i)

%o SET q,k*2*p(i)^2+1

%o PRP q,t

%o IF ISPRP THEN WRITE myf,t

%o IF ISPRP THEN GOTO a

%o GOTO b

%Y Cf. A224489, A224490, A224491, A224492, A224494, A224495, A224496.

%K nonn

%O 1,1

%A _Pierre CAMI_, Apr 08 2013