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A135274
a(n) = prime(2*n) - prime(2*n-1) + prime(2*n+1).
3
6, 13, 19, 25, 37, 47, 49, 65, 69, 77, 89, 103, 107, 113, 131, 141, 151, 159, 173, 185, 193, 199, 213, 239, 235, 247, 267, 275, 279, 287, 317, 317, 335, 353, 355, 373, 385, 393, 409, 427, 433, 441, 453, 469, 469, 499, 503, 513, 535, 565
OFFSET
1,1
COMMENTS
Original name was: Difference and sum of staircase primes according to the rule: bottom - top + next top.
We list the primes in staircase fashion as follows.
2
3.5
..7.11
....13.17
.......19.23
..........29.31
.............37.41
.....................
....................n
....................n+1.n+2.
The right diagonal, RD(n), is the set of top primes and the left diagonal, LD(x), is the set of bottom primes. Then a(n) = LD(n+1) - RD(n) + RD(n+2).
LINKS
FORMULA
a(n) = A181428(2*n-1). - R. J. Mathar, Sep 10 2016
MATHEMATICA
Join[{6}, #[[3]]-#[[2]]+#[[4]]&/@Partition[Prime[Range[2, 110]], 4, 2]] (* Harvey P. Dale, Nov 16 2011 *)
PROG
(PARI) g(n) = forstep(x=1, n, 2, y=prime(x+1)-prime(x)+prime(x+2); print1(y", "))
(PARI) a(n)=prime(2*n)-prime(2*n-1)+prime(2*n+1); \\ Joerg Arndt, Oct 08 2016
CROSSREFS
Sequence in context: A013575 A075727 A246306 * A189378 A022388 A041471
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Dec 02 2007
EXTENSIONS
New name from Joerg Arndt, Oct 08 2016
STATUS
approved