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