A233468 The digital root of prime(n+1) minus the digital root of prime(n).

1, 2, 2, -5, 2, 4, -7, 4, -3, 2, -3, 4, 2, -5, 6, -3, 2, -3, 4, -7, 6, -5, 6, -1, -5, 2, 4, -7, 4, -4, 4, -3, 2, 1, 2, -3, -3, 4, -3, 6, -7, 1, 2, 4, -7, 3, 3, -5, 2, 4, -3, 2, 1, -3, -3, 6, -7, 6, -5, 2, 1, -4, 4, 2, -5, 5, -3, 1, 2, -5, 6

Offset: 1

Author

Conner L. Delahanty, Apr 18 2014

Keywords

• base
• sign
• easy

Examples

			For n = 1, (prime(2) mod 9) - (prime(1) mod 9) =  3 (mod 9) - 2 (mod 9) = 3-2 = 1.
For n = 2, (prime(3) mod 9) - (prime(2) mod 9) =  5 (mod 9) - 3 (mod 9) = 5-3 = 2.
For n = 3, (prime(4) mod 9) - (prime(3) mod 9) =  7 (mod 9) - 5 (mod 9) = 7-5 = 2.
For n = 4, (prime(5) mod 9) - (prime(4) mod 9) = 11 (mod 9) - 7 (mod 9) = 2-7 = -5.
		

Links

• Conner L. Delahanty, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000040, A010888.

Programs

Maple

A233468:=n->(ithprime(n+1) mod 9) - (ithprime(n) mod 9); seq(A233468(n), n=1..100); # Wesley Ivan Hurt, Apr 19 2014

Mathematica

Table[Mod[Prime[n + 1], 9] - Mod[Prime[n], 9], {n, 100}] (* Wesley Ivan Hurt, Apr 19 2014 *)

Python

dd=[]
def prim(end):
    num=3
    primes=[2, 3]
    while (len(primes)<=end):
        num+=1
        prime=False
        length=len(primes)
        for y in range(0, length):
            if (num % primes[y]!=0):
                prime=True
            else:
                prime=False
                break
        if (prime):
            primes.append(num)
    for x in range(len(primes)-1):
        dd.append((primes[x+1]%9) - (primes[x]%9))
    return dd

Formula

a(n) = (prime(n+1) mod 9) - (prime(n) mod 9).

a(n) = prime(n + 1) - 9*floor((prime(n + 1) - 1)/9) - prime(n) + 9*floor((prime(n) - 1)/9). - Wesley Ivan Hurt, Apr 19 2014

a(n) = A010888(A000040(n+1)) - A010888(A000040(n)). - Michel Marcus, Apr 19 2014