A369022 a(n) is the least start of a run of exactly n consecutive integers with the same maximal exponent in their prime factorization, or -1 if no such run exists.

1, 2, 5, 844, 30923, 671346, 8870025

Offset: 1

Author

Amiram Eldar, Jan 12 2024

Keywords

• nonn
• hard
• more

Comments

a(8) > 3.7*10^10.

a(8) <= 1770019255373287038727484868192109228824 which is the conjectured value of A219452(8)+1. - Giorgos Kalogeropoulos, Jan 15 2024

Crossrefs

Cf. A051903, A369020, A369021.

Similar sequences: A071125, A219452, A323253.

Programs

Mathematica

emax[n_] := Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; ind = Position[Differences[Table[emax[n], {n, 1, 10^6}]], _?(# != 0 &)] // Flatten; d = Differences[ind]; seq = {1}; Do[i = FirstPosition[d, k]; If[MissingQ[i], Break[]]; AppendTo[seq, ind[[i[[1]]]] + 1], {k, 2, Max[d]}]; seq

PARI

emax(n) = vecmax(factor(n)[, 2]);
lista(len) = {my(v = vector(len), w = [0], m, c = 0, k = 2); while(c < len, e = emax(k); m = #w; if(e == w[m], w = concat(w, e), if(m < = len && v[m] == 0, v[m] = k-m; c++); w = [e]); k++); v;}

Formula

A051903(a(n)) >= k for 2^k <= n < 2^(k+1)-1.