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
Programs
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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.
Comments