A280008 First differences of A002375.

0, 1, 0, 1, -1, 1, 0, 0, 0, 1, 0, 0, -1, 1, -1, 2, 0, -2, 1, 1, -1, 1, 1, -1, -1, 2, -2, 1, 2, -3, 2, 1, -4, 3, 1, -1, 0, 2, -3, 1, 3, -3, -1, 5, -5, 1, 2, -4, 3, 2, -3, 1, 2, -2, 1, 3, -4, 0, 6, -8, 1, 5, -7, 4, 2, -3, -1, 3, -1, 1, 3, -5, -1, 7, -8, 4, 3, -6, 3, 2, -5, 1, 7, -4, -3, 5, -4, 0, 7, -8, 2, 5, -8, 3, 3, -4, 2, 4, -5, 1, 5, -7, 0, 12, -13, 2, 5, -6, 2, 2, -4, 0, 5, -3, -2, 8, -6, 0, 9, -10

Offset: 1

Author

Altug Alkan, Feb 21 2017

Keywords

• sign

Comments

See the perception of symmetry on scatterplot of this sequence that is also in Links section.

Are there infinitely many 0's in this sequence?

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Alternative Scatterplot of A280008

Crossrefs

Cf. A002375, A282778.

Programs

PARI

a002375(n) = sum(i=2, primepi(n), isprime(2*n - prime(i)));
a(n) = a002375(n+1) - a002375(n);

Formula

a(n) = A002375(n+1) - A002375(n).