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A243097 Digit sums of the nontrivial reversal numbers (numbers which are integer multiples of their reversal), excluding palindromes and multiples of 10.

%I A243097 #34 May 22 2025 10:21:38
%S A243097 18,18,27,27,36,36,45,45,36,54,36,54,36,63,36,63,36,54,72,36,54,72,36,
%T A243097 54,81,36,54,81,36,54,54,72,90,36,54,54,72,90,36,63,54,72,99,36,63,54,
%U A243097 72,99,36,54,72,54,72,72,90,108,36,54,72,54,72,72,90,108
%N A243097 Digit sums of the nontrivial reversal numbers (numbers which are integer multiples of their reversal), excluding palindromes and multiples of 10.
%F A243097 a(n) = 9(d-2p-b) where d is the number of digits in the reversal number, p is the number of repeating units of either 8712 or 9801 (they can be split in the middle of the sequence as long as all 4 numbers appear in the correct order), and b is the number of digits separating two complete "units" (must appear between two complete units and not in between 1 incomplete unit).
%F A243097 a(n) = A007953(A031877(n)).
%e A243097 a(1)=digit sum of 8712=8+7+1+2=18, a(3)=digit sum of 87912=8+7+9+1+2=27.
%o A243097 (Python)
%o A243097 A243097 = []
%o A243097 for n in range(1,10**7):
%o A243097     if n % 10:
%o A243097         s1 = str(n)
%o A243097         s2 = s1[::-1]
%o A243097         if s1 != s2 and not n % int(s2):
%o A243097             A243097.append(sum(int(d) for d in s1))
%o A243097 # _Chai Wah Wu_, Sep 05 2014
%Y A243097 Cf. A007953 (digit sum), A031877 (union of A222814 and A222815).
%K A243097 nonn,base
%O A243097 1,1
%A A243097 _Sam Mathers_, Aug 18 2014
%E A243097 More terms from _Michel Marcus_, Aug 25 2014