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A085876
Smallest k such that k and k+n have the same prime signature that is different from all previous terms.
2
2, 18, 35, 66, 4, 84, 344, 1692, 1785, 270, 4293, 1176, 9315, 1458, 3450, 5304, 2656, 10332, 8, 1352, 13344, 73040, 190762, 28812, 128180, 77248, 51948, 43092, 196, 35880, 287469, 85968, 387552, 83072, 412300, 45864, 247131, 549250, 1713855, 714960, 898816, 266448
OFFSET
1,1
EXAMPLE
a(1) = 2, as 2 and 2+1 = 3 both are primes.
a(2) = 18, 18 and 18+2 = 20 have the prime signature p^2*q.
a(4) = 66 as 66 + 4 = 70, both have prime signature p*q*r which has not occurred earlier.
a(19) = 8 as 8+19 = 27 and 8 and 27 have the same prime signature p^3.
PROG
(PARI) used = vector(42); ps(n) = local(f); f = factor(n); vecsort(f[, 2]);
a(n) = local(P, m, v, found, j); P = vector(n, i, ps(i)); m = 1; while (1, for (i = 1, n, v = ps(m*n + i); if (v == P[i], found = 0; j = 1; while (!found && j < n, if (v == used[j], found = 1, j++)); if (!found, used[n] = v; return((m - 1)*n + i))); P[i] = v); m++);
for (i = 1, 42, print1(a(i), ", ")); \\ David Wasserman, Jul 19 2005
CROSSREFS
Cf. A086489.
Sequence in context: A166259 A073213 A086490 * A099904 A137308 A050594
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jul 07 2003
EXTENSIONS
More terms from Ray Chandler, Jul 11 2003
More terms from Ray Chandler, Jul 13 2003
More terms from Michel Marcus, Sep 23 2023
STATUS
approved