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A181413 a(n) is the smallest number such that a(n)^2 + 1 is divisible by A002144(1)* A002144(2)*...* A002144(n).

%I A181413 #10 Feb 01 2019 11:17:27
%S A181413 2,8,47,2163,18543,241727,3101272,842894268,8245041748,521781374353,
%T A181413 101476250977928,671795954794788,32126984574675193,425090834074746637,
%U A181413 309609468228403885693,25836182225971546313682,38544366727563360743217,217758730168965028986551783,25789605237863389220212237968,309600287787935978580674202007
%N A181413 a(n) is the smallest number such that a(n)^2 + 1 is divisible by A002144(1)* A002144(2)*...* A002144(n).
%e A181413 a(1) = 2 because A002144(1) | 2^2+1 = 5 ;
%e A181413 a(2)=8 because A002144(1) * A002144(2) | 8^2+1 = 5*13 ;
%e A181413 a(6) = 241727 because A002144(1) * A002144(2)*...* A002144(6) | 241727^2+1
%e A181413   = 2 * 5 * 13 * 17 * 29 * 37 * 41 * 601.
%p A181413 with(numtheory):nn:=1000:T:=array(1..1000):k:=1:for x from 1 to nn do: p:=4*x+1:if
%p A181413   type(p, prime)=true then T[k]:=p:k:=k+1:else fi:od:pr:=1:for n from 1 to k do:
%p A181413   pp:=pr*T[n] :ind:=0:for q from 1 to pp while (ind=0) do: z:=q^2+1:if irem(z,pp)=0
%p A181413   and ind = 0 then ind: = 1:pr:=pp:print( q):else fi:od:od:
%p A181413 # Alternative
%p A181413 PP:= select(isprime, [seq(i,i=5..200,4)]):
%p A181413 f:= n -> min(map(t -> rhs(op(t)),[msolve(x^2+1, convert(PP[1..n],`*`))])):
%p A181413 map(f, [$1..20]); # _Robert Israel_, Feb 01 2019
%Y A181413 Cf. A002144 (Pythagorean primes: primes of form 4n+1) A002731.
%K A181413 nonn
%O A181413 1,1
%A A181413 _Michel Lagneau_, Jan 28 2011
%E A181413 More terms from _Robert Israel_, Feb 01 2019