cp's OEIS Frontend

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

%I A085876 #9 Sep 23 2023 03:39:22
%S A085876 2,18,35,66,4,84,344,1692,1785,270,4293,1176,9315,1458,3450,5304,2656,
%T A085876 10332,8,1352,13344,73040,190762,28812,128180,77248,51948,43092,196,
%U A085876 35880,287469,85968,387552,83072,412300,45864,247131,549250,1713855,714960,898816,266448
%N A085876 Smallest k such that k and k+n have the same prime signature that is different from all previous terms.
%e A085876 a(1) = 2, as 2 and 2+1 = 3 both are primes.
%e A085876 a(2) = 18, 18 and 18+2 = 20 have the prime signature p^2*q.
%e A085876 a(4) = 66 as 66 + 4 = 70, both have prime signature p*q*r which has not occurred earlier.
%e A085876 a(19) = 8 as 8+19 = 27 and 8 and 27 have the same prime signature p^3.
%o A085876 (PARI) used = vector(42); ps(n) = local(f); f = factor(n); vecsort(f[,2]);
%o A085876 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++);
%o A085876 for (i = 1, 42, print1(a(i), ", ")); \\ _David Wasserman_, Jul 19 2005
%Y A085876 Cf. A086489.
%K A085876 nonn
%O A085876 1,1
%A A085876 _Amarnath Murthy_, Jul 07 2003
%E A085876 More terms from _Ray Chandler_, Jul 11 2003
%E A085876 More terms from _Ray Chandler_, Jul 13 2003
%E A085876 More terms from _Michel Marcus_, Sep 23 2023