OFFSET
1,1
COMMENTS
The start of the least run of 4 (and also 5) consecutive integers with this property is 3988418748.
The numbers of terms that do not exceed 10^k, for k = 5, 6, ..., are 1, 18, 178, 1783, 17845, 178458, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00001784... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
71874 = 2 * 3^3 * 11^3 is a term since it is divisible by 3^3, 71875 = 5^5 * 23 is divisible by 5^5, and 71876 = 2^2 * 7 * 17 * 151 is divisible by 2^2.
MATHEMATICA
q[n_] := q[n] = AnyTrue[FactorInteger[n], First[#] <= Last[#] &]; Select[Range[2*10^6], q[#] && q[#+1] && q[#+2] &]
PROG
(PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1] <= f[i, 2], return(1))); 0; }
lista(kmax) = {my(is1 = 0, is2 = 0, is3); for(k = 3, kmax, is3 = is(k); if(is1 && is2 && is3, print1(k-2, ", ")); is1 = is2; is2 = is3); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 23 2024
STATUS
approved