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A154723
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Triangle read by rows in which row n lists all the pairs of non-composite numbers that are equidistant from n, or only n if there are no such pairs, as shown below in the example.
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13
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1, 1, 3, 1, 5, 1, 3, 5, 7, 3, 7, 1, 5, 7, 11, 1, 3, 11, 13, 3, 5, 11, 13, 1, 5, 7, 11, 13, 17, 1, 3, 7, 13, 17, 19, 3, 5, 17, 19, 1, 5, 7, 11, 13, 17, 19, 23, 3, 7, 19, 23, 5, 11, 17, 23, 1, 7, 11, 13, 17, 19, 23, 29, 1, 3, 13, 19, 29, 31, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| If the extended Goldbach conjecture is true, such a pair exists in row n for all n >= 2. - Nathaniel Johnston, Apr 18 2011
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..8000
Wolfram MathWorld, Goldbach Conjecture
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EXAMPLE
| Triangle begins:
. . . . . . . . . . . . . . .1
. . . . . . . . . . . . . 1, .. 3
. . . . . . . . . . . .1, .. .. .. 5
. . . . . . . . . . 1, .. 3, .. 5, .. 7
. . . . . . . . . . .. 3, .. .. .. 7, .. .
. . . . . . . 1, .. .. .. 5, .. 7, .. .. .,11
. . . . . .1, .. 3, .. .. .. .. .. .. ..11, ..13
. . . . .. .. 3, .. 5, .. .. .. .. ..11, ..13, .. .
. . .1, .. .. .. 5, .. 7, .. .. ..11, ..13, .. .. ..17
. 1, .. 3, .. .. .. 7, .. .. .. .. ..13, .. .. ..17, ..19
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MAPLE
| isnotcomp:=proc(n)return (n=1 or isprime(n)) end:
print(1):for n from 1 to 10 do for k from 1 to 2*n-1 do if(not k=n and (isnotcomp(k) and isnotcomp(2*n-k)))then print(k):fi:od:od: # Nathaniel Johnston, Apr 18 2011
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CROSSREFS
| Cf. A000040, A008578, A154720, A154721, A154722, A154724, A154725, A154726, A154727.
Sequence in context: A016475 A037227 A056753 * A114567 A001051 A046730
Adjacent sequences: A154720 A154721 A154722 * A154724 A154725 A154726
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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(36) - a(70) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 18 2011
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