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

Author

N. J. A. Sloane, Mar 13 2013

Keywords

• nonn
• tabf

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).

Examples

			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
 ...
		

References

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

Links

• 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.
• N. J. A. Sloane, 2178 And All That [Local copy]
• Anne Ludington Young, k-Reverse multiples, Fib. Q., 30 (1992), 126-132.

Crossrefs

Cf. A214927, A222817, A222819, A222820.

See A214927 for other cross-references.