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Jacobsthal Number

The Jacobsthal numbers are the numbers obtained by the s in the Lucas sequence with and , corresponding to and . They and the Jacobsthal-Lucas numbers (the s) satisfy the recurrence relation(1)The Jacobsthal numbers satisfy and and are 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ... (OEIS A001045). The Jacobsthal-Lucas numbers satisfy and and are 2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, ... (OEIS A014551). The properties of these numbers are summarized in Horadam (1996).Microcontrollers (and other computers) use conditional instructions to change the flow of execution of a program. In addition to branch instructions, some microcontrollers use skip instructions which conditionally bypass the next instruction. This winds up being useful for one case out of the four possibilities on 2 bits, 3 cases on 3 bits, 5 cases on 4 bits, 11 on 5 bits, 21 on 6 bits, 43 on 7 bits, 85 on 8 bits, ..., which are exactly the Jacobsthal numbers (Hirst 2006).The Jacobsthal..

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