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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.
8
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
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
Sequence in context: A357751 A046558 A180854 * A172022 A152967 A376433
KEYWORD
nonn,easy
EXTENSIONS
More terms from Erich Friedman
STATUS
approved