A222817 Irregular triangle read by rows: row n gives list of nontrivial reverse multipliers for base n.

2, 3, 2, 4, 2, 5, 3, 6, 2, 3, 5, 7, 2, 4, 8, 4, 9, 2, 3, 5, 7, 10, 2, 3, 5, 11, 5, 6, 12, 2, 3, 4, 6, 9, 13, 2, 3, 4, 7, 11, 14, 3, 7, 15, 2, 4, 5, 8, 10, 11, 16, 2, 5, 7, 8, 17, 3, 4, 6, 7, 9, 14, 18, 2, 3, 4, 6, 9, 13, 19

Offset

3,1

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 excluded.

The last entry in each row is n-1; the number of terms in row n is A222819(n).

Links

Table of n, a(n) for n=3..72.

N. J. A. Sloane, Table giving n,  list of nontrivial reverse multipliers, for n = 3..100

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:
  2,
  3,
  2,4,
  2,5,
  3,6,
  2,3,5,7,
  2,4,8,
  4,9,
  2,3,5,7,10,
  2,3,5,11,
  5,6,12,
  2,3,4,6,9,13,
  2,3,4,7,11,14,
  3,7,15,
  ...

Crossrefs

Cf. A214927, A222818, A222819, A222820.

See A214927 for other cross-references.

Sequence in context: A365791 A331252 A162908 * A344324 A309428 A328368

Adjacent sequences: A222814 A222815 A222816 * A222818 A222819 A222820

Keyword

nonn,tabf

Author

N. J. A. Sloane, Mar 13 2013

Status

approved