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A154727
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Triangle read by rows in which row n lists all the pairs of prime numbers that are equidistant from n, or only n if there is no such pair, as shown below in the example.
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13
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1, 2, 3, 3, 5, 3, 7, 5, 7, 3, 11, 3, 5, 11, 13, 5, 7, 11, 13, 3, 7, 13, 17, 3, 5, 17, 19, 5, 7, 11, 13, 17, 19, 3, 7, 19, 23, 5, 11, 17, 23, 7, 11, 13, 17, 19, 23, 3, 13, 19, 29, 3, 5, 11, 23, 29, 31, 5, 7, 13, 17, 19, 23, 29, 31, 7, 31, 3, 11, 17
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If the extended Goldbach conjecture is true, such a pair exists in row n for all n >= 4. - Nathaniel Johnston, Apr 18 2011
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LINKS
| Wolfram MathWorld, Goldbach Conjecture
Nathaniel Johnston, Table of n, a(n) for n = 1..10000
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EXAMPLE
| Triangle begins:
. . . . . . . . . . . . . 1
. . . . . . . . . . . . . 2
. . . . . . . . . . . . . 3
. . . . . . . . . . . .3, .. 5
. . . . . . . . . . 3, .. .. .. 7
. . . . . . . . . . .. 5, .. 7, .. .
. . . . . . . 3, .. .. .. .. .. .. ..11
. . . . . .3, .. 5, .. .. .. .. . 11, ..13
. . . . .. .. 5, .. 7, .. .. . 11, . 13, .. .
. . .3, .. .. .. 7, .. .. .. .. . 13, .. .. ..17
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MAPLE
| print(1):print(2):print(3):for n from 1 to 15 do for k from 1 to 2*n-1 do if(not k=n and (isprime(k) and isprime(2*n-k)))then print(k):fi:od:od: # Nathaniel Johnston, Apr 18 2011
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CROSSREFS
| Cf. A000040, A154720, A154721, A154722, A154723, A154724, A154725, A154726.
Sequence in context: A177980 A064921 A064917 * A065070 A070800 A138663
Adjacent sequences: A154724 A154725 A154726 * A154728 A154729 A154730
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KEYWORD
| easy,nonn,tabf
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Jan 14 2009, Jan 16 2009
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EXTENSIONS
| a(24) - a(70) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 18 2011
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