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
Examples
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.
Programs
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Mathematica
Mod[Accumulate[Join[{0}, Prime[Range[105]]]], 10] (* Amiram Eldar, Mar 09 2025 *) -
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
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
Extensions
a(0) = 0 inserted and new name by Michel Marcus, Mar 09 2025
Comments