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

Author

Amarnath Murthy, Jul 07 2003

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A086489.

Programs

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

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