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a(1)=1; at n>=2, a(n) = least square > a(n-1) such that sum a(1)+...+a(n) is a prime number.
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%I #10 Jan 27 2023 19:04:45

%S 1,4,36,576,1296,1764,2304,4356,6084,15876,19044,20736,26244,44100,

%T 69696,76176,82944,86436,112896,152100,176400,213444,248004,254016,

%U 260100,285156,291600,324900,381924,396900,412164,435600,476100,492804,553536,608400,705600

%N a(1)=1; at n>=2, a(n) = least square > a(n-1) such that sum a(1)+...+a(n) is a prime number.

%H Zak Seidov, <a href="/A139033/b139033.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = A137326(n)^2.

%t s={1};su=1;Do[p=su+n^2;If[PrimeQ[p],su=p;AppendTo[s,n^2]],{n,2,120000}];s

%Y Cf. A137326, A139034 (corresponding primes).

%K nonn

%O 1,2

%A _Zak Seidov_, Apr 07 2008

%E Edited by _Alois P. Heinz_, Jan 27 2023