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A135274
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Difference and sum of staircase primes according to the rule: bottom - top + next top.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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).
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MATHEMATICA
| Join[{6}, #[[3]]-#[[2]]+#[[4]]&/@Partition[Prime[Range[2, 110]], 4, 2]] (* From Harvey P. Dale, Nov 16 2011 *)
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PROG
| (PARI) g(n) = forstep(x=1, n, 2, y=prime(x+1)-prime(x)+prime(x+2); print1(y", "))
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CROSSREFS
| Sequence in context: A095911 A013575 A075727 * A189378 A022388 A041471
Adjacent sequences: A135271 A135272 A135273 * A135275 A135276 A135277
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KEYWORD
| nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)hotmail.com), Dec 02 2007
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