A364805 a(n) is the smallest number k such that the number of distinct prime divisors of the n numbers from k through k+n-1 are in nondescending order.

1, 1, 1, 1, 1, 1, 141, 141, 211, 211, 82321, 82321, 526093, 526093, 526093, 526093, 127890361, 127890361

Offset: 1

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

• nonn
• more

Comments

Smallest initial number k of n consecutive numbers satisfying omega(k) <= omega(k+1) <= ... <= omega(k+n-1).

Examples

			a(9) = 211 = a(10) as omega(211) = 1 < omega(212) = omega(213) = omega(214) = omega(215) = omega(216) = omega(217) = omega(218) = omega(219) = 2 < omega(220) = 3.
		

Crossrefs

Cf. A001221, A075046, A286287, A364804.

Programs

Mathematica

k = 1; Do[While[t = Table[PrimeNu[i], {i, k, k + n - 1}]; t != Sort[t], k++]; Print[k], {n, 1, 16}]

PARI

a(n) = my(k=1, list=List(vector(n, i, omega(i)))); while (vecsort(list) != list, listpop(list, 1); k++; listput(list, omega(k+n-1))); k; \\ Michel Marcus, Aug 14 2023

Extensions

a(17)-a(18) from Michel Marcus, Aug 14 2023