cp's OEIS Frontend

A249430 a(n) = Least integer k such that A249431(k) = n, and -1 if no such integer exists.

%I A249430 #23 Aug 28 2025 00:04:57
%S A249430 1,0,350,439,174,713,323,1923,1052,999,1766,3749,2254,2253,1934,3391,
%T A249430 4184,4463,3144,5451,9698,16279,6398,5123,2974,12863,19094,4299,16574,
%U A249430 5749
%N A249430 a(n) = Least integer k such that A249431(k) = n, and -1 if no such integer exists.
%C A249430 a(n) = the least natural number k such that {product of elements on row k of Pascal's triangle} is divisible by (k+n)! but not by (k+n+1)!
%C A249430 Note: a(18) = 3144 and a(24) = 2974. First values k for which A249431(k) = 16 and 17, if they exist, are larger than 4096.
%o A249430 (Scheme) (define (A249430 n) (let loop ((k 0)) (cond ((= n (A249431 k)) k) (else (loop (+ 1 k))))))
%o A249430 (Python)
%o A249430 from itertools import count
%o A249430 from math import factorial
%o A249430 def A249430(n):
%o A249430     f = factorial(n)
%o A249430     g = f*(n+1)
%o A249430     pascal = [1]
%o A249430     for k in count(0):
%o A249430         a = 1
%o A249430         for i in range(k+1):
%o A249430             a = a*pascal[i]%f
%o A249430         if not a:
%o A249430             b = 1
%o A249430             for i in range(k+1):
%o A249430                 b = b*pascal[i]%g
%o A249430             if b:
%o A249430                 return k
%o A249430         f = g
%o A249430         g *= k+n+2
%o A249430         pascal = [1]+[pascal[i]+pascal[i+1] for i in range(k)]+[1] # _Chai Wah Wu_, Aug 18 2025
%Y A249430 Nonnegative terms are all members of A249434.
%Y A249430 Cf. A000142, A001142, A007318, A249151, A249431, A249432.
%K A249430 nonn,more,changed
%O A249430 0,3
%A A249430 _Antti Karttunen_, Nov 02 2014
%E A249430 a(16)-a(20) from _Chai Wah Wu_, Aug 19 2025
%E A249430 a(21)-a(29) from _Chai Wah Wu_, Aug 27 2025