A096316 Given the number wheel 0,1,2,3,4,5,6,7,8,9 then starting with 2, the next number is a prime p number of positions from the previous number found, for p=2,3,...

4, 7, 2, 9, 0, 3, 0, 9, 2, 1, 2, 9, 0, 3, 0, 3, 2, 3, 0, 1, 4, 3, 6, 5, 2, 3, 6, 3, 2, 5, 2, 3, 0, 9, 8, 9, 6, 9, 6, 9, 8, 9, 0, 3, 0, 9, 0, 3, 0, 9, 2, 1, 2, 3, 0, 3, 2, 3, 0, 1, 4, 7, 4, 5, 8, 5, 6, 3, 0, 9, 2, 1, 8, 1, 0, 3, 2, 9, 0, 9, 8, 9, 0, 3, 2, 5, 4, 1, 2, 5, 2, 1, 8, 9, 8, 1, 0, 1, 4, 5, 2, 9, 2, 1, 2

Offset

0,1

Comments

Conjecture: This sequence carried to infinity is non-repeating and non-terminating. If we concatenate the numbers and introduce a decimal point somewhere, we will get an irrational number.

Links

Table of n, a(n) for n=0..104.

Formula

n=2, n = (n mod 10 + p)%10 where p is prime = 2, 3, 5...

Example

Imagine a number wheel 0,1,2,3,4,5,6,7,8,9 like the numbers on an odometer. The first prime in the wheel is 2. Counting from 2, the next number is 2 positions beyond 2 which is 4; counting 3 positions from 4, we get 7; counting 5 positions from 7 (when we hit 9, we go to 0) we get 2. 4,7,2 are the first 3 terms in the table.

Mathematica

a[-2] = 2; a[n_] := a[n] = Mod[a[n - 1] + Prime[n + 2], 10]; Array[a, 105, -1] (* Robert G. Wilson v, Mar 10 2013 *)

Prog

(PARI) f(n) = x=2; forprime(p=2, n, x=(x%10+p)%10; print1(x", "))

Crossrefs

Cf. A096319.

Sequence in context: A362753 A194160 A154466 * A010777 A336050 A103887

Adjacent sequences: A096313 A096314 A096315 * A096317 A096318 A096319

Keyword

easy,nonn

Author

Cino Hilliard, Aug 02 2004

Status

approved