A243590 Numbers returned when each digit of n is replaced by the sum modulo 10 of the digits to its (wrapped) left and (wrapped) right.

2, 4, 6, 8, 0, 2, 4, 6, 8, 2, 22, 42, 62, 82, 2, 22, 42, 62, 82, 4, 24, 44, 64, 84, 4, 24, 44, 64, 84, 6, 26, 46, 66, 86, 6, 26, 46, 66, 86, 8, 28, 48, 68, 88, 8, 28, 48, 68, 88, 0, 20, 40, 60, 80, 0, 20, 40, 60, 80, 2, 22, 42, 62, 82, 2, 22, 42, 62, 82, 4, 24

Offset: 1

Author

Anthony Sand, Jun 07 2014

Keywords

• nonn
• base

Comments

Numbers returned by the following function: take the t digits of n, d(1)..d(t), and replace each with the sum d(i) = (d(i-1) + d(i+1)) mod 10, where (i-1 = 0) maps to t and (i+1 > t) maps to 1.

Examples

			For 1, the function returns (1 + 1) mod 10 = 2.
For 5, the function returns (5 + 5) mod 10 = 0.
For 125, the initial digits are (1,2,5).
d(1) <- (d(3) + d(2)) mod 10 = (5 + 2) mod 10 = 7; d(2) <- (d(1) + d(3)) mod 10 = (1 + 5) mod 10 = 6; d(3) <- (d(2) + d(1)) mod 10 = (2 + 1) mod 10 = 3.
The function returns (7,6,3) = 763.
		

Links

• Anthony Sand, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055120, A035327.

Formula

for digits d(1)..d(t), d(i) = (d(i-1) + d(i+1)) mod 10, where (i-1 = 0) -> t, (i+1 > t) -> 1.