A333453 Binary concatenation (ignoring leading zeros) of a(n-1) and a(n-2) mod n, starting with a(n) = n for n <= 1.

0, 1, 1, 0, 1, 1, 3, 0, 3, 3, 5, 1, 1, 3, 7, 1, 15, 14, 5, 18, 9, 12, 3, 14, 11, 15, 17, 17, 1, 20, 11, 0, 11, 11, 17, 3, 5, 23, 37, 37, 5, 29, 27, 33, 27, 6, 35, 4, 3, 28, 15, 49, 19, 46, 33, 13, 25, 14, 9, 40, 49, 4, 57, 19, 57, 23, 11, 40, 39, 52, 7, 3, 31

Offset: 0

Author

Alois P. Heinz, Mar 21 2020

Keywords

• nonn
• base

Comments

Value 0 is treated as empty bit string.

Examples

			a(18) = 5 = 239 mod 18, where 239 = 11101111_2 is the binary concatenation 1110_2 = 14 = a(17) and 1111_2 = 15 = a(16).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..32768

Crossrefs

Cf. A062383, A063896, A079777.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n, (t-> a(n-1)*
      `if`(t=0, 1, 2^(ilog2(t)+1))+t)(a(n-2)) mod n)
    end:
seq(a(n), n=0..100);

Formula

a(n) = (a(n-1)*A062383(a(n-2)) + a(n-2)) mod n if n > 1, a(n) = n if n < 2.