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A309655
The smallest possible nonnegative difference between the sum of the first n primes (A007504) and the sum of any number of the directly following and consecutive primes.
1
0, 2, 0, 3, 6, 15, 5, 16, 25, 3, 20, 39, 13, 36, 61, 17, 50, 6, 39, 76, 14, 53, 102, 28, 75, 132, 46, 101, 158, 46, 99, 174, 64, 145, 27, 114, 193, 51, 144, 239, 93, 194, 24, 135, 244, 74, 179, 294, 116, 253, 43, 162, 291, 61, 196, 337, 101, 250, 395, 139, 282, 427, 149, 324
OFFSET
0,2
COMMENTS
Conjecture: a(0)=0, a(2)=0 and a(532)=0 are the only zeros in the sequence. a(n) has been computed for primes < 10^10. - Bob Andriesse, Oct 07 2020
EXAMPLE
a(2) = 2 + 3 - 5 = 0;
a(3) = 2 + 3 + 5 - 7 = 3;
a(6) = 2 + 3 + 5 + 7 + 11 + 13 - (17 + 19) = 5.
a(532)=0 because A007504(733) = 2*A007504(532).
PROG
(Python)
#Lists a(1)...a(100)
from sympy import prime
sumP=0
for i in range(1, 101):
sumP+=prime(i)
j=i+1
diff=sumP
while diff-prime(j) >=0:
diff-=prime(j)
j+=1
print diff, ', ',
CROSSREFS
Sequence in context: A248966 A021495 A332356 * A260591 A127160 A334847
KEYWORD
nonn
AUTHOR
Bob Andriesse, Aug 11 2019
STATUS
approved