A305238 Negative numbers in base -10.

19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 79, 78, 77, 76, 75

Offset: 1

Author

Jianing Song, Jun 19 2018

Keywords

• nonn
• base
• easy

Comments

a(n) = A039723(-n).

Also base -10 representation of -n reinterpreted as decimal numbers.

The first comment is slightly misleading because sequence A039723 isn't defined for n < 0, and none of the terms a(n) here is a term of A039723. However, it can be seen as the definition of the extension of A039723 to negative indices. Also, the (naïve) recursive definition or implementation of A039723 requires that function to be defined for negative arguments, and using the generic formula it will work as expected for -n, n > 0. - M. F. Hasler, Oct 16 2018

Examples

			-1 in base -10 is represented as 19 (1*(-10) + 9 = -1), so a(1) = 19;
-11 in base -10 is represented as 29 (2*(-10) + 9 = -11), so a(11) = 29;
-99 in base -10 is represented as 1901 (1*(-10)^3 + 9*(-10)^2 + 1 = -99), so a(99) = 1901.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Negadecimal
• Eric Weisstein's World of Mathematics, Negabinary
• Wikipedia, Negative base

Crossrefs

Cf. A039724 (nonnegative numbers in base -2), A212529 (negative numbers in base -2), A007608 (nonnegative numbers in base -4), A212526 (negative numbers in base -4), A039723 (nonnegative numbers in base -10).

Programs

PARI

A305238(n)=A039723(-n) \\ M. F. Hasler, Oct 16 2018