cp's OEIS Frontend

A367740 a(n) = A367727(A367593(n)).

%I A367740 #35 Dec 02 2023 01:41:50
%S A367740 -1,0,0,0,5,0,9,5,0,5,0,5,0,5,3,0,5,0,8,5,0,8,5,0,8,5,3,0,8,5,0,8,5,3,
%T A367740 0,8,5,0,8,5,3,0,8,5
%N A367740 a(n) = A367727(A367593(n)).
%C A367740 Restricted to integers k where k + 1 divides R(k) - 1 the terms are (R(k) - 1) / (k + 1), where R(k) denotes the digit reversal of k. - _Peter Luschny_, Dec 01 2023
%C A367740 The 0's correspond to the powers of 10 (cf. A011557), the 5's correspond to the numbers of the form 14*10^h + 7 = 7*A199682(h) for h > 0, and the 8's correspond to the numbers of the form 12345*10^m + 6789 = A367650(m) for m > 3. The only negative term -1 corresponds to A367593(1) = 0. - _Stefano Spezia_, Dec 01 2023
%F A367740 -1 <= a(n) <= 9.
%o A367740 (Python)
%o A367740 def A367740List(upto):
%o A367740     L = []
%o A367740     for n in range(upto):
%o A367740         rev = int(str(n)[::-1])
%o A367740         if (rev - 1) % (n + 1) == 0:
%o A367740             L.append((rev - 1) // (n + 1))
%o A367740     return L
%o A367740 print(A367740List(10**6))  # _Peter Luschny_, Dec 01 2023
%o A367740 (Python)
%o A367740 from itertools import product, count, islice
%o A367740 def A367740_gen(): # generator of terms
%o A367740     yield from (-1,0,0)
%o A367740     for l in count(1):
%o A367740         m = 10**(l+1)
%o A367740         for d in product('0123456789',repeat=l):
%o A367740             for a, b, c in ((1, 0, 0), (1, 1, 0), (1, 4, 2), (1, 5, 5), (1, 7, 5)):
%o A367740                 k = a*m+int(s:=''.join(d))*10+b
%o A367740                 r = b*m+int(s[::-1])*10+a
%o A367740                 if c*(k+1)==r-1:
%o A367740                     yield c
%o A367740             a,b = 1,9
%o A367740             k = a*m+int(s:=''.join(d))*10+b
%o A367740             r = b*m+int(s[::-1])*10+a
%o A367740             p,q = divmod(r-1,k+1)
%o A367740             if not q:
%o A367740                 yield p
%o A367740         a,b,c=2,6,3
%o A367740         for d in product('0123456789',repeat=l):
%o A367740             k = a*m+int(s:=''.join(d))*10+b
%o A367740             r = b*m+int(s[::-1])*10+a
%o A367740             if c*(k+1)==r-1:
%o A367740                 yield c
%o A367740 A367740_list = list(islice(A367740_gen(),20)) # _Chai Wah Wu_, Dec 01 2023
%Y A367740 Cf. A367593, A367727, A367728.
%Y A367740 Cf. A004086, A011557, A199682, A367650.
%K A367740 sign,base,hard,more
%O A367740 1,5
%A A367740 _Stefano Spezia_, Nov 29 2023
%E A367740 a(30)-a(44) from _Chai Wah Wu_, Dec 02 2023