A014687 In sequence of odd primes add 1 to first prime, 3rd prime, 5th prime, ... then subtract 1 from 2nd prime, fourth prime, sixth prime and so on.

4, 4, 8, 10, 14, 16, 20, 22, 30, 30, 38, 40, 44, 46, 54, 58, 62, 66, 72, 72, 80, 82, 90, 96, 102, 102, 108, 108, 114, 126, 132, 136, 140, 148, 152, 156, 164, 166, 174, 178, 182, 190, 194, 196, 200, 210, 224, 226, 230, 232, 240, 240, 252, 256, 264, 268, 272, 276

Offset: 1

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Examples

			a(4) + a(3) = 10 + 8 = 18 = prime(4) + prime(5) = 7 + 11.
		

Crossrefs

Cf. A000040, A033999.

Programs

Mathematica

a[1]=4; a[n_] := a[n]=Prime[n]+Prime[n+1]-a[n-1]
Total/@Partition[Riffle[Prime[Range[2,60]],{1,-1}],2] (* Harvey P. Dale, May 19 2011 *)

Formula

a(n) = prime(n+1) + (-1)^(n+1). - Juri-Stepan Gerasimov, Sep 10 2009

a(n) = odd prime(n) - (-1)^n. - Juri-Stepan Gerasimov, Sep 10 2009

a(n) + a(n-1) = prime(n) + prime(n+1), i.e., a(n) = prime(n) + prime(n+1) - a(n-1) generates sequence with initial value a(1)=4. - Labos Elemer, Apr 24 2003; corrected by Dean Hickerson, Apr 27 2003

a(n) = A000040(n+1) - A033999(n+1). - Juri-Stepan Gerasimov, Sep 10 2009

Extensions

More terms from Erich Friedman