A162735 An alternating sum of all numbers from prime(n) to prime(n+1).

1, 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129, 134, 138, 144, 150, 154, 160, 165, 170, 176, 180, 186, 192, 195, 198, 205, 217, 225, 228, 231, 236, 240, 246, 254, 260, 266, 270, 274, 279

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 13 2009

Keywords

• nonn

Comments

Without the initial term, identical to A024675, cf. formula. Except for the initial terms, also the same as A162800. - M. F. Hasler, Jun 01 2013

Examples

			a(1) = 1 = -2+3. a(2) = 4=3-4+5. a(3) = 6 =5-6+7. a(4) = 9 = 7-8+9-10+11.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A024675, A162800.

Programs

Mathematica

Join[{1}, Most[#] + Differences[#]/2] & [Prime[Range[2, 100]]] (* Paolo Xausa, Jun 17 2024 *)

Formula

a(n) = sum_{j= A000040(n).. A000040(n+1)} (-1)^(j+1)*j = A001057(A000040(n+1))-A001057(A000040(n)-1).

{1} U A024675.

Extensions

Edited by R. J. Mathar, Sep 23 2009