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A181429 a(n)= the smallest number such that a(n)^2+1=p*A002144(n), p prime.

%I A181429 #5 Mar 30 2012 18:35:54
%S A181429 3,5,30,12,80,9,30,11,46,34,22,414,76,15,100,44,28,80,19,274,380,794,
%T A181429 144,64,530,456,60,334,724,25,114,526,136,42,104,274,334,1584,266,29,
%U A181429 254,516,566,48,810,286,52,2110,86,1130,516,726,35,194,154,504,106,58,4036,566,96,380
%N A181429 a(n)= the smallest number such that a(n)^2+1=p*A002144(n), p prime.
%e A181429 a(1) = 3 because 3^2+1 = 2*A002144(1) = 2*5 ;
%e A181429 a(2) = 5 because 5^2+1 = 2*A002144(2) = 2*13 ;
%e A181429 a(3) = 30 because 30^2+1 = 53*A002144(3)  = 53*17;
%e A181429 a(4) = 12 because 12^2+1 = 5*A002144(4) = 5*29.
%p A181429 with(numtheory):nn:=10000:T:=array(1..10000):k:=2:T[1]:=2:for x from 1 to nn
%p A181429   do: p:=4*x+1:if type(p, prime)=true then T[k]:=p:k:=k+1:else fi:od:for n from
%p A181429   2 to 100 do: id:=0:for p from 1 to k while(id=0) do:x:=T[n]*T[p]-1:y:=sqrt(x):if
%p A181429   y=floor(y)then id:=1:printf(`%d, `,y):else fi:od:od:
%Y A181429 Cf. A002144.
%K A181429 nonn
%O A181429 1,1
%A A181429 _Michel Lagneau_, Jan 29 2011