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A073852 a(1) = 1, then smallest square not included earlier such that every partial sum is a prime.

%I A073852 #10 Apr 09 2023 02:06:00
%S A073852 1,4,36,576,144,2916,324,1296,900,2304,3600,7056,1764,8100,4356,5184,
%T A073852 9216,6084,14400,15876,10404,22500,20736,11664,24336,12996,19044,
%U A073852 17424,32400,41616,44100,28224,34596,36864,54756,30276,26244,46656,39204
%N A073852 a(1) = 1, then smallest square not included earlier such that every partial sum is a prime.
%H A073852 Robert Israel, <a href="/A073852/b073852.txt">Table of n, a(n) for n = 1..10000</a>
%p A073852 R:= 1: cands:= [seq(i^2,i=2..10^6)]: nc:= 10^6-1: s:= 1: found:= true:
%p A073852 for n from 2 to 100 while found do
%p A073852   found:= false;
%p A073852   for j from 1 to nc do
%p A073852     if isprime(s+cands[j]) then
%p A073852       found:= true; R:= R, cands[j];
%p A073852       s:= s+cands[j];
%p A073852       cands:= subsop(j=NULL,cands);
%p A073852       break
%p A073852     fi
%p A073852 od od:
%p A073852 R; # _Robert Israel_, Apr 09 2023
%o A073852 (PARI) v=[1]; n=1; while(n<10^3, if(isprime(n^2+vecsum(v))&&!vecsearch(vecsort(v), n^2), v=concat(v, n^2); n=1); n++); v \\ _Derek Orr_, Jun 06 2015
%Y A073852 Cf. A073854.
%K A073852 nonn,easy
%O A073852 1,2
%A A073852 _Amarnath Murthy_, Aug 15 2002
%E A073852 Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 24 2003