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A351855 Partial sums of nonsquares that are partial sums of nonprimes.

%I A351855 #31 Apr 05 2022 17:06:35
%S A351855 5,64,506,64325,268723,480129,6282620,64548862,9657523883,13480852825,
%T A351855 29766135708,105223301080,519861666225,851245744041,1378216791896,
%U A351855 581522966976875,583298551668358,885441628670251,1651966084813205,16868988672306046,17170433482837259
%N A351855 Partial sums of nonsquares that are partial sums of nonprimes.
%H A351855 Chai Wah Wu, <a href="/A351855/b351855.txt">Table of n, a(n) for n = 1..26</a>
%e A351855 a(2) = 64 is a term because 64 = 1+4+6+8+9+10+12+14 = 2+3+5+6+7+8+10+11+12 is the sum of the first 8 nonprimes and the sum of the first 9 nonsquares.
%p A351855 i:= 0: j:= 0: s:= 0: t:= 0:
%p A351855 R:= NULL: count:= 0:
%p A351855 while count < 13 do
%p A351855   if s <= t then
%p A351855      i:= i+1;
%p A351855      if not issqr(i) then
%p A351855        s:= s+i;
%p A351855        if s=t then R:= R,s; count:= count+1 fi;
%p A351855      fi
%p A351855   else
%p A351855      j:= j+1;
%p A351855      if not isprime(j) then
%p A351855        t:= t+j;
%p A351855        if s=t then R:= R,t; count:= count+1 fi;
%p A351855      fi
%p A351855   fi
%p A351855 od:
%p A351855 R;
%o A351855 (Python)
%o A351855 from itertools import islice
%o A351855 from sympy import nextprime
%o A351855 def A351855_gen(): # generator of terms
%o A351855     c, k, ks, m, p, q = 0, 1, 2, 1, 4, 5
%o A351855     while True:
%o A351855         for n in range(ks,ks+2*k):
%o A351855             c += n
%o A351855             if c == m:
%o A351855                 yield c
%o A351855             else:
%o A351855                 while c > m:
%o A351855                     m += p
%o A351855                     p += 1
%o A351855                     if p == q:
%o A351855                         q = nextprime(q)
%o A351855                         p += 1
%o A351855         ks += 2*k+1
%o A351855         k += 1
%o A351855 A351855_list = list(islice(A351855_gen(),20)) # _Chai Wah Wu_, Apr 04 2022
%Y A351855 Intersection of A051349 and A086849.
%K A351855 nonn
%O A351855 1,1
%A A351855 _J. M. Bergot_ and _Robert Israel_, Mar 31 2022
%E A351855 a(20)-a(21) from _Jon E. Schoenfield_, Mar 31 2022