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a(n) is the number of reverse multipliers for base n.
5

%I #26 Jan 09 2025 10:17:25

%S 1,2,2,3,3,3,5,4,3,6,5,4,7,7,4,8,6,8,8,7,6,11,11,6,8,9,6,13,12,10,13,

%T 6,9,14,10,9,13,17,9,15,12,13,17,13,11,20,16,12,12

%N a(n) is the number of reverse multipliers for base n.

%C If there is a number m such that the reversal of m in base n is c times m, then c is called a reverse multiplier for n. For example, 2 is a reverse multiplier for base n=5, since 8 (base 10) = 13 (base 5), and 2*8 = 16 (base 10) = 31 (base 5).

%C The trivial reverse multiplier 1 is included.

%C a(n)-1 is the length of row n of A222817. - _Michel Marcus_, Apr 12 2020

%D For a complete list of references and links related to this problem see A214927.

%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1307.0453">2178 And All That</a>, arXiv:1307.0453 [math.NT], 2013; see <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/52-2/Sloan10242013.pdf">also</a>, Fib. Quart., 52 (2014), 99-120.

%H N. J. A. Sloane, <a href="/A001232/a001232.pdf">2178 And All That</a> [Local copy]

%H Anne Ludington Young, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/30-2/ludington1.pdf">k-Reverse multiples</a>, Fib. Q., 30 (1992), 126-132.

%Y Cf. A214927, A222817, A222818, A222819.

%Y See A214927 for other cross-references.

%K nonn,more,base

%O 2,2

%A _N. J. A. Sloane_, Mar 13 2013