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Search: id:A109860
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| A109860 |
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Triangle whose n-th row contains the next n numbers relatively prime to n! and not occurring in a previous row. a(1) = 1. |
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+0
2
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| 1, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209, 211, 221, 223, 227, 229, 233, 239
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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1
3 5
7 11 13
17 19 23 25
29 31 37 41 43
47 49 53 59 61 67
71 73 79 83 89 97 101
...
2 is the only prime that is not a member. Conjecture: There are finitely many composite terms.
The sequence contains infinitely many composites. Through n rows, there are ~ n^2/2 terms. The number of primes up to (n+1)^2 is ~ n^2/(2 log n), which is eventually quite a bit less. Most products of two nearby primes will be in the sequence. Frank Adams-Watters (FrankTAW(at)Netscape.net), Apr 14 2006
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CROSSREFS
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Cf. A109861.
Sequence in context: A003255 A118749 A122089 this_sequence A100392 A067019 A132106
Adjacent sequences: A109857 A109858 A109859 this_sequence A109861 A109862 A109863
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KEYWORD
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nonn,tabl
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 08 2005
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EXTENSIONS
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Corrected, extended, and edited by Frank Adams-Watters (FrankTAW(at)Netscape.net), Apr 14 2006
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