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A184995
Irregular triangle T, read by rows, in which row n lists the primes p <= n such that 2n-p is also prime.
6
2, 3, 3, 3, 5, 5, 3, 7, 3, 5, 5, 7, 3, 7, 3, 5, 11, 5, 7, 11, 3, 7, 13, 5, 11, 7, 11, 13, 3, 13, 3, 5, 11, 17, 5, 7, 13, 17, 7, 19, 3, 11, 17, 5, 11, 13, 19, 3, 7, 13, 3, 5, 17, 23, 5, 7, 11, 17, 19, 3, 7, 13, 19, 5, 11, 23, 7, 11, 13, 17, 23, 3, 13, 19, 5, 11, 17, 29, 7, 13, 17, 19, 23, 29
OFFSET
2,1
COMMENTS
Row n has first entry A020481(n), length A045917(n), and last entry A112823(n).
Each row is the prefix to the middle of the corresponding row of A171637.
The Goldbach conjecture states that this irregular Goldbach triangle has in each row at least one entry (A045917(n) >= 1). - Wolfdieter Lang, May 14 2016
FORMULA
T(n,i) = n - A182138(n,i). - Jason Kimberley, Sep 25 2012
EXAMPLE
The irregular triangle T(n, i) starts:
n, 2*n\i 1 2 3 4 5 6 ...
2, 4 2
3, 6 3
4, 8 3
5, 10 3 5
6, 12 5
7, 14 3 7
8, 16 3 5
9, 18 5 7
10, 20 3 7
11, 22 3 5 11
12, 24 5 7 11
13, 26 3 7 13
14, 28 5 11
15, 30 7 11 13
16, 32 3 13
17, 34 3 5 11 17
18, 36 5 7 13 17
19, 38 7 19
20, 40 3 11 17
21, 42 5 11 13 19
22, 44 3 7 13
23, 46 3 5 17 23
24, 48 5 7 11 17 19
25, 50 3 7 13 19
26, 52 5 11 23
27, 54 7 11 13 17 23
28, 56 3 13 19
29, 58 5 11 17 29
30, 60 7 13 17 19 23 29
... reformatted - Wolfdieter Lang, May 14 2016
MATHEMATICA
Table[Select[Prime@ Range@ PrimePi@ n, PrimeQ[2 n - #] &], {n, 2, 30}] // Flatten (* Michael De Vlieger, May 14 2016 *)
PROG
(Magma) A184995 := func<n|[p:p in PrimesUpTo(n)|IsPrime(2*n-p)]>;
&cat[A184995(n):n in [2..30]];
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Jason Kimberley, Sep 03 2011
STATUS
approved