A351855 - OEIS

%I #31 Apr 05 2022 17:06:35

%S 5,64,506,64325,268723,480129,6282620,64548862,9657523883,13480852825,

%T 29766135708,105223301080,519861666225,851245744041,1378216791896,

%U 581522966976875,583298551668358,885441628670251,1651966084813205,16868988672306046,17170433482837259

%N Partial sums of nonsquares that are partial sums of nonprimes.

%H Chai Wah Wu, <a href="/A351855/b351855.txt">Table of n, a(n) for n = 1..26</a>

%e 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 i:= 0: j:= 0: s:= 0: t:= 0:

%p R:= NULL: count:= 0:

%p while count < 13 do

%p   if s <= t then

%p      i:= i+1;

%p      if not issqr(i) then

%p        s:= s+i;

%p        if s=t then R:= R,s; count:= count+1 fi;

%p      fi

%p   else

%p      j:= j+1;

%p      if not isprime(j) then

%p        t:= t+j;

%p        if s=t then R:= R,t; count:= count+1 fi;

%p      fi

%p   fi

%p od:

%p R;

%o (Python)

%o from itertools import islice

%o from sympy import nextprime

%o def A351855_gen(): # generator of terms

%o     c, k, ks, m, p, q = 0, 1, 2, 1, 4, 5

%o     while True:

%o         for n in range(ks,ks+2*k):

%o             c += n

%o             if c == m:

%o                 yield c

%o             else:

%o                 while c > m:

%o                     m += p

%o                     p += 1

%o                     if p == q:

%o                         q = nextprime(q)

%o                         p += 1

%o         ks += 2*k+1

%o         k += 1

%o A351855_list = list(islice(A351855_gen(),20)) # _Chai Wah Wu_, Apr 04 2022

%Y Intersection of A051349 and A086849.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 31 2022

%E a(20)-a(21) from _Jon E. Schoenfield_, Mar 31 2022