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

1,1

Links

Table of n, a(n) for n=1..64.

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)).

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A010857 A369860 A158910 * A040307 A022352 A211411

Adjacent sequences: A243094 A243095 A243096 * A243098 A243099 A243100

Keyword

nonn,base

Author

Sam Mathers, Aug 18 2014

Extensions

More terms from Michel Marcus, Aug 25 2014

Status

approved