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A249432 Positions of records in A249431.

%I A249432 #17 Aug 19 2025 18:10:41
%S A249432 0,174,323,999,1766,1934,2974,4299,5749,9974,15685,25478,31406
%N A249432 Positions of records in A249431.
%C A249432 The corresponding record values in A249431 are: 1, 4, 6, 9, 10, 14, 24, ...
%C A249432 Larger terms could be found by searching large prime gaps: A249431(31406) = 62, and any number k such that A249431(k) >= 63 must have nextprime(k) - k > 63. - _Charlie Neder_, May 24 2019
%o A249432 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A249432 (define A249432 (RECORD-POS 1 0 A249431))
%o A249432 (Python)
%o A249432 from itertools import count, islice
%o A249432 from collections import Counter
%o A249432 from math import comb
%o A249432 from sympy import factorint
%o A249432 def A249432_gen(): # generator of terms
%o A249432     c = -1
%o A249432     for n in count(0):
%o A249432         p = sum((Counter(factorint(comb(n,i))) for i in range(n+1)),start=Counter())
%o A249432         for m in count(1):
%o A249432             f = Counter(factorint(m))
%o A249432             if not f<=p:
%o A249432                 break
%o A249432             p -= f
%o A249432         if (k:=m-1-n)>c:
%o A249432             yield n
%o A249432             c = k
%o A249432 A249432_list = list(islice(A249432_gen(),4)) # _Chai Wah Wu_, Aug 19 2025
%Y A249432 Subsequence of A249434 and A249430.
%Y A249432 Cf. A249151, A249431, A249430.
%K A249432 nonn,more
%O A249432 1,2
%A A249432 _Antti Karttunen_, Nov 02 2014
%E A249432 a(8)-a(13) from _Charlie Neder_, May 24 2019