OFFSET

1,1

COMMENTS

Numbers k such that k, k+1 and k+2 are all terms of A283050.

Numbers of the form 4*k+2 are not terms of A283050. Therefore, there are no runs of 4 or more consecutive integers, and all the terms of this sequence are of the form 4*k+3.

The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 2, 40, 429, 4419, 44352, 444053, 4441769, 44421000, 444220814, ... . Apparently, the asymptotic density of this sequence exists and equals 0.004442... .

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

423 is a term since 3 is the least prime factor of 423 and 423 is divisible by 3^2 = 9, 2 is the least prime factor of 424 and 424 is divisible by 2^2 = 4, and 5 is the least prime factor of 425 and 425 is divisible by 5^2 = 25.

MATHEMATICA

Select[4 * Range[2700] + 3, AllTrue[# + {0, 1, 2}, FactorInteger[#1][[1, -1]] >= 2 &] &]

SequencePosition[Table[If[Divisible[n, FactorInteger[n][[1, 1]]^2], 1, 0], {n, 11000}], {1, 1, 1}][[;; , 1]] (* Harvey P. Dale, Aug 05 2024 *)

PROG

(PARI) is(n) = factor(n)[1, 2] >= 2;

lista(kmax) = forstep(k = 3, kmax, 4, if(is(k) && is(k+1) && is(k+2), print1(k, ", ")));

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Sep 21 2023

STATUS

approved