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

18, 18, 27, 27, 36, 36, 45, 45, 36, 54, 36, 54, 36, 63, 36, 63, 36, 54, 72, 36, 54, 72, 36, 54, 81, 36, 54, 81, 36, 54, 54, 72, 90, 36, 54, 54, 72, 90, 36, 63, 54, 72, 99, 36, 63, 54, 72, 99, 36, 54, 72, 54, 72, 72, 90, 108, 36, 54, 72, 54, 72, 72, 90, 108

Offset: 1

Author

Sam Mathers, Aug 18 2014

Keywords

• nonn
• base

Examples

			a(1)=digit sum of 8712=8+7+1+2=18, a(3)=digit sum of 87912=8+7+9+1+2=27.
		

Crossrefs

Cf. A007953 (digit sum), A031877 (union of A222814 and A222815).

Programs

Python

A243097 = []
for n in range(1,10**7):
    if n % 10:
        s1 = str(n)
        s2 = s1[::-1]
        if s1 != s2 and not n % int(s2):
            A243097.append(sum(int(d) for d in s1))
# Chai Wah Wu, Sep 05 2014

Formula

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).

a(n) = A007953(A031877(n)).

Extensions

More terms from Michel Marcus, Aug 25 2014