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A333688
Partial sums of A070748.
1
1, 2, 1, 2, 1, 2, 1, 2, 1, 0, -1, -2, -3, -4, -3, -2, -1, -2, -3, -2, -3, -4, -3, -2, -1, 0, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, -1, -2, -1, -2, -1, -2, -1, -2, -3, -2, -1, 0, 1, 2, 3, 2, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, -2, -1, -2
OFFSET
1,2
COMMENTS
This sequence counts what the prime number distribution is in the intervals where the sine function gives different signs: if a(n) is positive, it means that up to n more primes fall into the interval (2k*Pi, (2k+1)*Pi) than in ((2k+1)*Pi, (2k+2)*Pi) for k=0,1,2,3... When a(n) is zero, the first n primes are distributed equally between these intervals.
LINKS
FORMULA
a(n) = Sum_{k=1..n} A070748(k). - Sean A. Irvine, May 02 2020
EXAMPLE
For n=4, a(4) = signum(sin(2)) + signum(sin(3)) + signum(sin(5)) + signum(sin(7)) = 1 + 1 - 1 + 1 = 2.
MATHEMATICA
Accumulate @ Table[Sign @ Sin @ Prime[i], {i, 1, 70}] (* Amiram Eldar, Apr 02 2020 *)
PROG
(MATLAB)
primes_up_to=1000;
sequence(1)=1;
for n=2:1:primes_up_to
if isprime(n)
sequence(numel(primes(n)))=sum(sign(sin(primes(n))));
end
end
result=transpose((sequence));
(PARI) a(n) = sum(k=1, n, sign(sin(prime(k)))); \\ Michel Marcus, May 03 2020
CROSSREFS
Sequence in context: A341945 A280535 A221171 * A319610 A288739 A111621
KEYWORD
sign
AUTHOR
Bence Bernáth, Apr 02 2020
STATUS
approved