A275771 a(n+3) = A008578(n+1) -a(n), a(0) = a(1) = a(2) = 0.

0, 0, 0, 1, 2, 3, 4, 5, 8, 9, 12, 11, 14, 17, 20, 23, 24, 23, 24, 29, 36, 37, 38, 35, 36, 41, 48, 53, 56, 53, 50, 51, 56, 63, 76, 75, 74, 63, 74, 77, 94, 89, 90, 79, 90, 91, 112, 103, 106, 87, 108, 117, 140

Offset: 0

Author

Paul Curtz, Aug 08 2016

Keywords

• nonn

Comments

A008578 gives the noncomposite numbers, the prime numbers at the beginning of the 20th century which included 1.

a(2n) = 0, 0, 2, 4, 8, 12, 14, 20, 24, 24, ... always even?

a(2n+3) = 1, 3, 5, 9, 11, 17, 23, 23, 29, ... always odd?

First differences: 0, 0, 1, 1, 1, 1, 1, 3, 1, 3, -1, 3, 3, 3, 3, 1, -1, 1, 5, 7, ... .

Examples

			a(3) = 1-0 = 1, a(4) = 2-0 = 2, a(5) = 3-0 = 3, a(6) = 5-1 = 4, a(6) = 7-2 = 5, ... .
		

Crossrefs

Cf. A000040, A008578, A113405, A274817.

Programs

Mathematica

RecurrenceTable[{a[n + 3] == If[n == 0, 1, Prime[n]] - a[n], a[0] == 0, a[1] == 0, a[2] == 0}, a, {n, 0, 52}] (* Michael De Vlieger, Aug 08 2016 *)