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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 (list; graph; refs; listen; history; text; internal format)
 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 Bence Bernáth, Table of n, a(n) for n = 1..10000 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 Cf. A007504, A070748. Sequence in context: A341945 A280535 A221171 * A319610 A288739 A111621 Adjacent sequences:  A333685 A333686 A333687 * A333689 A333690 A333691 KEYWORD sign AUTHOR Bence Bernáth, Apr 02 2020 STATUS approved

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Last modified September 18 11:38 EDT 2021. Contains 347527 sequences. (Running on oeis4.)