A364804 a(n) is the smallest number k such that the number of prime divisors (counted with multiplicity) of the n numbers from k through k+n-1 are in nondescending order.

1, 1, 1, 1, 121, 121, 2521, 2521, 162121, 460801, 23553169, 23553169, 244068841, 913535283

Offset: 1

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

• nonn
• more

Comments

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

Examples

			a(5) = 121 = a(6) as bigomega(121) = bigomega(122) = bigomega(123) = 2 < bigomega(124) = bigomega(125) = 3 < bigomega(126) = 4.
		

Crossrefs

Cf. A001222, A075046, A286288, A364805.

Programs

Mathematica

k = 1; Do[While[t = Table[PrimeOmega[i], {i, k, k + n - 1}]; t != Sort[t], k++]; Print[k], {n, 1, 10}]

PARI

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

Extensions

a(11)-a(14) from Michel Marcus, Aug 14 2023