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A222818 Irregular triangle read by rows: row n gives list of reverse multipliers for base n.

%I A222818 #23 Jan 09 2025 10:18:01
%S A222818 1,1,2,1,3,1,2,4,1,2,5,1,3,6,1,2,3,5,7,1,2,4,8,1,4,9,1,2,3,5,7,10,1,2,
%T A222818 3,5,11,1,5,6,12,1,2,3,4,6,9,13,1,2,3,4,7,11,14,1,3,7,15,1,2,4,5,8,10,
%U A222818 11,16,1,2,5,7,8,17,1,3,4,6,7,9,14,18,1,2,3,4,6,9,13,19
%N A222818 Irregular triangle read by rows: row n gives list of reverse multipliers for base n.
%C A222818 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 A222818 The trivial reverse multiplier 1 is included.
%C A222818 The last entry in each row is n-1; the number of terms in row n is A222820(n).
%D A222818 For a complete list of references and links related to this problem see A214927.
%H A222818 N. J. A. Sloane, <a href="/A222817/a222817.txt">Table giving n, number of nontrivial reverse multipliers, list of nontrivial reverse multipliers, for n = 3..50</a>
%H A222818 N. J. A. Sloane, <a href="http://arxiv.org/abs/1307.0453">2178 And All That</a>, arXiv:1307.0453 [math.NT], 2013; Fib. Quart., 52 (2014), 99-120.
%H A222818 N. J. A. Sloane, <a href="/A001232/a001232.pdf">2178 And All That</a> [Local copy]
%H A222818 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.
%e A222818 Triangle begins:
%e A222818   1,
%e A222818   1,2,
%e A222818   1,3,
%e A222818   1,2,4,
%e A222818   1,2,5,
%e A222818   1,3,6,
%e A222818   1,2,3,5,7,
%e A222818   1,2,4,8,
%e A222818   1,4,9,
%e A222818   1,2,3,5,7,10,
%e A222818   1,2,3,5,11,
%e A222818   1,5,6,12,
%e A222818   1,2,3,4,6,9,13,
%e A222818   1,2,3,4,7,11,14,
%e A222818   1,3,7,15
%e A222818  ...
%Y A222818 Cf. A214927, A222817, A222819, A222820.
%Y A222818 See A214927 for other cross-references.
%K A222818 nonn,tabf
%O A222818 2,3
%A A222818 _N. J. A. Sloane_, Mar 13 2013