login
A083129
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.
1
2, 2, 3, 4, 7, 9, 11, 338, 525, 9651, 5355, 12459, 99748, 29108, 375427, 58083, 5164682, 36679164, 105060351, 199616700, 860020506, 419164596, 9239876720, 37677869739
OFFSET
1,1
COMMENTS
First of the smallest set of n consecutive numbers each one divisible by a distinct prime chosen from among the first n primes.
EXAMPLE
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.
PROG
(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));
CROSSREFS
Cf. A083130.
Sequence in context: A345867 A252796 A083130 * A365090 A110160 A277252
KEYWORD
nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 23 2003
EXTENSIONS
Corrected and extended by David Wasserman, Oct 20 2004
STATUS
approved