A096319 Final digit of the sum of the first n primes.

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

Offset

0,2

Comments

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

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..105.

Formula

a(n) = (a(n-1) + prime(n)) mod 10, with a(0) = 0.

a(n) = A007504(n) mod 10. - Michel Marcus, Mar 09 2025

Example

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

Mathematica

Mod[Accumulate[Join[{0}, Prime[Range[105]]]], 10] (* Amiram Eldar, Mar 09 2025 *)

Prog

(PARI) \\ number max of p, m = starting position.
wheel(n, m) = { x=m; forprime(p=2, n, x=(x + p)%10; print1(x", ") ) }
(PARI) a(n) = lift(vecsum(apply(x->Mod(x, 10), primes(n)))); \\ Michel Marcus, Mar 09 2025

Crossrefs

Cf. A096316, A096320.

Cf. A010879, A007504.

Sequence in context: A011184 A157214 A066033 * A146105 A331165 A022832

Adjacent sequences: A096316 A096317 A096318 * A096320 A096321 A096322

Keyword

easy,nonn,base,changed

Author

Cino Hilliard, Aug 02 2004

Extensions

a(0) = 0 inserted and new name by Michel Marcus, Mar 09 2025

Status

approved