Binary signed-digit integers and the Stern diatomic sequence

Stern’s diatomic sequence is a well-studied and simply defined with many fascinating characteristics. The binary signed-digit representation of integers an alternative much use in efficient computation, coding theory cryptography. We link these two ideas here, showing that the number i-bit representations integer n $$n<2^i$$ $$(2^i-n)^{\text {th}}$$ element sequence. This correspondence makes vast range results known for available consideration study integers.