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

1,1

Links

Table of n, a(n) for n=1..58.

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

Example

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

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 *)

Crossrefs

Cf. A000040, A033999.

Sequence in context: A357751 A046558 A180854 * A172022 A152967 A301705

Adjacent sequences: A014684 A014685 A014686 * A014688 A014689 A014690

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Erich Friedman

Status

approved