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a(n) is the start of the least run of exactly n consecutive numbers with the same value of A349258.
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%I #6 Nov 12 2021 12:22:27

%S 1,14,20,2,91,6850,2302,141,56014,184171,2800171,27805034,35297611,

%T 8313366182,1791416073,3618621410

%N a(n) is the start of the least run of exactly n consecutive numbers with the same value of A349258.

%C a(17) > 10^11, if it exists.

%e a(2) = 14 since A349258(14) = A349258(15) = 2, but A349258(13) != 2 and A349258(16) != 2.

%t f[p_, e_] := 2^DigitCount[e, 2, 1] - 1; d[1] = 0; d[n_] := Plus @@ f @@@ FactorInteger[n]; seq[len_, nmax_] := Module[{s = Table[0, {len}], dprev = 0, n = 2, c = 1, k = 1}, s[[1]] = 1; While[k < len && n < nmax, d1 = d[n]; If[d1 == dprev, c++, If[c > 0 && c <= len && s[[c]] == 0, k++; s[[c]] = n - c]; c = 1]; n++; dprev = d1]; TakeWhile[s, # > 0 &]]; seq[8, 10^4]

%Y Cf. A349258.

%Y Similar sequences: A006558, A045983, A048932, A067813, A077657, A318166.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Nov 12 2021