A085876 Smallest k such that k and k+n have the same prime signature that is different from all previous terms.

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

Links

Table of n, a(n) for n=1..42.

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

Adjacent sequences: A085873 A085874 A085875 * A085877 A085878 A085879

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