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A101513
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a(1) = 1, a(2) = 2, a(3) = 3; triangle where n-th row has lowest n positive integers not yet in the sequence such that each integer has a prime divisor in common with at least one element of the (n-1)th row.
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3
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1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 5, 7, 15, 16, 18, 20, 21, 22, 24, 25, 26, 11, 13, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 17, 19, 45, 46, 48, 49, 50, 51, 52, 23, 54, 55, 56, 57, 58, 60, 62, 63, 64, 29, 31, 65, 66, 68, 69, 70, 72, 74, 75, 76, 37, 77, 78, 80, 81, 82
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Is this a permutation of the positive integers?
Conjectures from N. J. A. Sloane (njas(AT)research.att.com), Apr 22, 2005:
"Call a number "postponed" if it cannot be placed right away, that is, if it is relatively prime to the numbers in the previous row. Then I conjecture that:
"(1) a number n >= 4 is postponed iff n is prime,
"(2) every number appears,
"(3) the primes appear in order,
"(4) 2p (p prime) will appear in one row and p will appear in the next row,
"(5) let c(i) = A018252(i) be the i-th nonprime and define a sequence k(n) [see A104655], n >= 3, by k(3) = 4 and for n >= 4, n*(n+1)/2 = pi( floor( c(k(n-1))/2 ) ) + k(n). Then the final term in row n, for n >= 3, is c(k(n)) [A104656]."
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EXAMPLE
| Triangle begins:
1
2 3
4 6 8
9 10 12 14
5 7 15 16 18
20 21 22 24 25 26
11 13 27 28 30 32 33
...
7 is in the 5th row because it does not occur earlier and 14 is in the 4th row.
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CROSSREFS
| Cf. the EKG sequence A064413. See also A104654, A104655, A104656.
Sequence in context: A026433 A015858 A125292 * A153276 A108408 A173905
Adjacent sequences: A101510 A101511 A101512 * A101514 A101515 A101516
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KEYWORD
| nonn,tabl
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AUTHOR
| Leroy Quet Jan 25 2005
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EXTENSIONS
| More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 20 2006
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