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%I #13 Jul 28 2023 16:01:13
%S 1,1,1,4,4,36,36,144,36,324,324,36,36,36,144,144,144,36,36,36,900,900,
%T 900,324,900,36,324,36,324,576,324,144,36,324,36,576,144,2304,576,36,
%U 144,900,324,144,576,324,900,36,144,900,2916,144,2916,36,576,900,1764,324,144,1296,36,36
%N a(0) = 1; afterwards a(n) is the smallest positive square that added to all previous terms produces a prime.
%C All terms starting with a(5) are multiples of 36.
%C a(n) exists for all n under the Hardy-Littlewood Conjecture F. - _Charles R Greathouse IV_, Nov 06 2014
%H Charles R Greathouse IV, <a href="/A249807/b249807.txt">Table of n, a(n) for n = 0..10000</a>
%e 1+1+1+4=7(prime), 7+4=11(prime), 11+36=47(prime), 47+36=83(prime).
%t nxt[{t_,a_}]:=Module[{k=1},While[!PrimeQ[t+k^2],k++];{t+k^2,k^2}]; NestList[nxt,{1,1},70][[;;,2]] (* _Harvey P. Dale_, Jul 28 2023 *)
%o (PARI) first(n)=n=max(n,5); my(v=vector(n+1,i,1),k,s=11); v[4]=v[5]=4; for(i=6,#v, k=6; while(!isprime(s+k^2), k+=6); s+=v[i]=k^2); v \\ _Charles R Greathouse IV_, Nov 06 2014
%Y Cf. A073609.
%K nonn,easy
%O 0,4
%A _Zak Seidov_, Nov 06 2014
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