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Search: id:A083129
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| A083129 |
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Consider the triangle in which n-th row contains the smallest set of n consecutive numbers such that every prime among first n primes divides at least one distinct number in the row (irrespective of order). Sequence gives the first column. |
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2
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| 2, 2, 3, 4, 7, 9, 11, 338, 525, 9651, 5355, 12459, 99748, 29108, 375427, 58083, 5164682, 36679164, 105060351, 199616700, 860020506, 419164596, 9239876720, 37677869739
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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First of the smallest set of n consecutive numbers each one divisible by a distinct prime chosen from among the first n primes.
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EXAMPLE
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2
2 3
3 4 5
4 5 6 7
7 8 9 10 11
9 10 11 12 13 14
11 12 13 14 15 16 17
...
a(8) = 338: 13|338, 3|339, 17|340, 11|341, 19|342, 7|343, 2|344, 5|345.
a(8) is not A083130(8) = 32 because in the numbers 32-39, 35 is the only multiple of 5 and the only multiple of 7, so these numbers can't be paired with the first 8 primes.
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PROGRAM
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(PARI) doIt(partial, current, n, used) = local(p, nextP, v); if (current < 1, leastFound = lift(partial), p = prime(current); for (i = 1, n, if (!used[i], nextP = chinese(Mod(-i, p), partial); if (lift(nextP) < leastFound, v = used; v[i] = 1; doIt(nextP, current - 1, n, v))))); for (j = 1, 30, leastFound = prime(j)^j; for (k = 1, j, v = vector(j); v[k] = 1; doIt(Mod(-k, prime(j)), j - 1, j, v)); print(leastFound + 1));
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CROSSREFS
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Cf. A083130.
Adjacent sequences: A083126 A083127 A083128 this_sequence A083130 A083131 A083132
Sequence in context: A091605 A125554 A083130 this_sequence A110160 A003179 A143590
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Apr 23 2003
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EXTENSIONS
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Corrected and extended by David Wasserman (wasserma(AT)spawar.navy.mil), Oct 20 2004
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