A162572 Decimal numbers n which, when converted to a lower number base, show the reversed digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 13, 23, 46, 445, 2116, 15226, 313725, 1527465, 3454446, 2426472326, 3066511287, 102461381175475216

Offset: 1

Author

Claudio Meller, Jul 06 2009

Keywords

• nonn
• base
• fini
• full

Comments

All entries lack the digit 9, because this digit is absent in the representations in bases 2 to 9.

The sequence is finite because for every n > 10^22 the representation of n in a base b < 10 has more digits than the representation of n in base 10. a(20) is the last term. - Giovanni Resta, Aug 13 2019

Examples

			13 is 31 in base 4. 23 is 32 in base 7. 46 is 64 in base 7.
801 is not a term since it is 1080 in base 9, so with an extra 0.
		

Crossrefs

Cf. A034294, A090144. - R. J. Mathar, Jul 17 2009

Programs

PARI

isok(n) = {my(d = digits(n)); for (b=2, 9, my(rd = Vecrev(digits(n, b))); if ((#rd == #d) && fromdigits(rd) == n, return (b)););} \\ Michel Marcus, Aug 05 2019

Extensions

Keyword:base, single-digit numbers and 313725 added by R. J. Mathar, Jul 17 2009

a(16)-a(17) from Michel Marcus, Aug 05 2019

a(18)-a(19) from Giovanni Resta, Aug 06 2019

a(20) from Giovanni Resta, Aug 13 2019