I have been trying for a logic for mapping a series which is
8->15 maps to 0-7
24->31 maps t0 8-15
40->47 maps to 16-23
and so on . I am given this sequence and a constant number =8. I can do subtraction, addition, multiplication , division etc. with series numbers and constant number. Trying hard since yesterday, can anyone tell me it is even possible?
Each number in your sequence on the left are precisely those numbers with a $1$ in the third digit (counting from the right) when represented in binary. (See http://oeis.org/A115419)
By considering the binary representation of your numbers, determine the result of your "mapping" by deleting the third digit. (By deleting, I mean completely remove it, not just replace it with zero).
E.g. $8$ which was $\color{red}{1}00_2$ becomes $00_2$ which is $0$ in decimal, $24$ which was $1\color{red}{1}00_2$ becomes $100_2$ which is $8$ in decimal, $29$ which was $11\color{red}{1}01_2$ becomes $1101_2$ which is $13$ in decimal, etc...
If you insist on this being notated with symbols rather than words, then we have $n\mapsto 8\lfloor\frac{n}{16}\rfloor + n-8\lfloor\frac{n}{8}\rfloor$