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

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

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 n-1; 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, arXiv:1307.0453 [math.NT], 2013; Fib. Quart., 52 (2014), 99-120.

Anne Ludington Young, k-Reverse multiples, Fib. Q., 30 (1992), 126-132.

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 cross-references.

Sequence in context: A301983 A373889 A165416 * A057059 A368313 A346795

Adjacent sequences: A222815 A222816 A222817 * A222819 A222820 A222821

Keyword

nonn,tabf

Author

N. J. A. Sloane, Mar 13 2013

Status

approved