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A253425 Lengths of runs of identical terms in A253415.

%I A253425 #17 Jan 25 2022 15:33:53
%S A253425 1,1,6,11,18,12,5,22,91,143,1,93,370,182,20,20,315,332,973,157,1223,
%T A253425 1807,325,4044,7412,11211,4600,2176,14848,4659,3123,10852,1678,20862,
%U A253425 3348
%N A253425 Lengths of runs of identical terms in A253415.
%t A253425 c[_] = 0; c[1] = j = 1; u = 2; s = 3; Most@ Tally[#][[All, -1]] &@ Reap[Do[d = Divisors[s]; k = 1; While[c[d[[k]]] > 0, k++]; Set[k, d[[k]]]; Set[c[k], i]; If[k == u, While[c[u] > 0, u++]]; Sow[u]; j = k; s += k, {i, 2, 2^12}]][[-1, -1]] (* _Michael De Vlieger_, Jan 23 2022 *)
%o A253425 (Haskell)
%o A253425 import Data.List (group)
%o A253425 a253425 n = a253425_list !! (n-1)
%o A253425 a253425_list = map length $ group a253415_list
%o A253425 (Python)
%o A253425 from itertools import islice
%o A253425 from sympy import divisors
%o A253425 def A253425_gen(): # generator of terms
%o A253425     bset, l, m, s = {1}, 0, 2, 3
%o A253425     while True:
%o A253425         for d in divisors(s):
%o A253425             if d not in bset:
%o A253425                 bset.add(d)
%o A253425                 if m in bset:
%o A253425                     yield l
%o A253425                     l = 1
%o A253425                     while m in bset:
%o A253425                         m += 1
%o A253425                 else:
%o A253425                     l += 1
%o A253425                 s += d
%o A253425                 break
%o A253425 A253425_list = list(islice(A253425_gen(),20)) # _Chai Wah Wu_, Jan 25 2022
%Y A253425 Cf. A253415, A095258.
%K A253425 nonn,more
%O A253425 1,3
%A A253425 _Reinhard Zumkeller_, Dec 31 2014
%E A253425 a(14)-a(35) from _Michael De Vlieger_, Jan 23 2022