A349261 a(n) is the least number k such that A349258(k) = A349258(k+1) = n.
2, 14, 125, 135, 2079, 21735, 2730375, 916352, 5955200, 4122495, 444741759, 7391633535, 98228219264
Offset: 1
Examples
2 is a term since A349258(2) = A349258(3) = 1. 14 is a term since A349258(14) = A349258(15) = 2.
Programs
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Mathematica
f[p_, e_] := 2^DigitCount[e, 2, 1] - 1; c[1] = 0; c[n_] := Plus @@ f @@@ FactorInteger[n]; seq[len_, nmax_] := Module[{s = Table[0, {len}], k = 0, n = 1, i}, While[n < nmax && k < len, i = c[n]; If[c[n + 1] == i && i <= len && s[[i]] == 0, k++; s[[i]] = n]; n++]; TakeWhile[s, # > 0 &]]; seq[8, 3*10^6]