

A222818


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


4



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, 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, 11, 16, 1, 2, 5, 7, 8, 17, 1, 3, 4, 6, 7, 9, 14, 18, 1, 2, 3, 4, 6, 9, 13, 19
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OFFSET

2,3


COMMENTS

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).
The trivial reverse multiplier 1 is included.
The last entry in each row is n1; the number of terms in row n is A222820(n).


REFERENCES

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


LINKS

Table of n, a(n) for n=2..90.
N. J. A. Sloane, Table giving n, number of nontrivial reverse multipliers, list of nontrivial reverse multipliers, for n = 3..50
N. J. A. Sloane, 2178 And All That, Fib. Quart., 52 (2014), 99120.
Anne Ludington Young, kReverse multiples, Fib. Q., 30 (1992), 126132.


EXAMPLE

Triangle begins:
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,
1,2,3,5,11,
1,5,6,12,
1,2,3,4,6,9,13,
1,2,3,4,7,11,14,
1,3,7,15
...


CROSSREFS

Cf. A214927, A222817, A222819, A222820.
See A214927 for other crossreferences.
Sequence in context: A304038 A301983 A165416 * A057059 A169896 A210208
Adjacent sequences: A222815 A222816 A222817 * A222819 A222820 A222821


KEYWORD

nonn,tabf


AUTHOR

N. J. A. Sloane, Mar 13 2013


STATUS

approved



