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A351855 Partial sums of nonsquares that are partial sums of nonprimes. 1
5, 64, 506, 64325, 268723, 480129, 6282620, 64548862, 9657523883, 13480852825, 29766135708, 105223301080, 519861666225, 851245744041, 1378216791896, 581522966976875, 583298551668358, 885441628670251, 1651966084813205, 16868988672306046, 17170433482837259 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..26

EXAMPLE

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.

MAPLE

i:= 0: j:= 0: s:= 0: t:= 0:

R:= NULL: count:= 0:

while count < 13 do

if s <= t then

i:= i+1;

if not issqr(i) then

s:= s+i;

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

fi

else

j:= j+1;

if not isprime(j) then

t:= t+j;

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

fi

fi

od:

R;

PROG

(Python)

from itertools import islice

from sympy import nextprime

def A351855_gen(): # generator of terms

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

while True:

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

c += n

if c == m:

yield c

else:

while c > m:

m += p

p += 1

if p == q:

q = nextprime(q)

p += 1

ks += 2*k+1

k += 1

A351855_list = list(islice(A351855_gen(), 20)) # Chai Wah Wu, Apr 04 2022

CROSSREFS

Intersection of A051349 and A086849.

Sequence in context: A193184 A180787 A222455 * A178295 A054937 A302993

Adjacent sequences: A351852 A351853 A351854 * A351856 A351857 A351858

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Mar 31 2022

EXTENSIONS

a(20)-a(21) from Jon E. Schoenfield, Mar 31 2022

STATUS

approved

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Last modified December 2 08:36 EST 2022. Contains 358493 sequences. (Running on oeis4.)