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A184995
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Irregular triangle T, read by rows, in which row n lists the primes p <= n such that 2n-p is also prime.
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6
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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
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OFFSET
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2,1
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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Table[Select[Prime@ Range@ PrimePi@ n, PrimeQ[2 n - #] &], {n, 2, 30}] // Flatten (* Michael De Vlieger, May 14 2016 *)
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PROG
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(Magma) A184995 := func<n|[p:p in PrimesUpTo(n)|IsPrime(2*n-p)]>;
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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