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A305238
Negative numbers in base -10.
4
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
1,1
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
LINKS
Eric Weisstein's World of Mathematics, Negadecimal
Eric Weisstein's World of Mathematics, Negabinary
Wikipedia, Negative base
EXAMPLE
-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.
PROG
(PARI) A305238(n)=A039723(-n) \\ M. F. Hasler, Oct 16 2018
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).
Sequence in context: A230339 A022975 A023461 * A004460 A082126 A176411
KEYWORD
nonn,base,easy
AUTHOR
Jianing Song, Jun 19 2018
STATUS
approved