A233468 - OEIS

%I #31 Apr 25 2014 21:37:06

%S 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,

%T 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,

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

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

%H Conner L. Delahanty, <a href="/A233468/b233468.txt">Table of n, a(n) for n = 1..20000</a>

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

%F 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

%F a(n) = A010888(A000040(n+1) - A010888(A000040(n). - _Michel Marcus_, Apr 19 2014

%e For n = 1, (prime(2) mod 9) - (prime(1) mod 9) =  3 (mod 9) - 2 (mod 9) = 3-2 = 1.

%e For n = 2, (prime(3) mod 9) - (prime(2) mod 9) =  5 (mod 9) - 3 (mod 9) = 5-3 = 2.

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

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

%p A233468:=n->(ithprime(n+1) mod 9) - (ithprime(n) mod 9); seq(A233468(n), n=1..100); # _Wesley Ivan Hurt_, Apr 19 2014

%t Table[Mod[Prime[n + 1], 9] - Mod[Prime[n], 9], {n, 100}] (* _Wesley Ivan Hurt_, Apr 19 2014 *)

%o (Python)

%o dd=[]

%o def prim(end):

%o ....num=3

%o ....primes=[2,3]

%o ....while (len(primes)<=end):

%o ........num+=1

%o ........prime=False

%o ........length=len(primes)

%o ........for y in range(0,length):

%o ............if (num % primes[y]!=0):

%o ................prime=True

%o ............else:

%o ................prime=False

%o ................break

%o ........if (prime):

%o ............primes.append(num)

%o ....for x in range(len(primes)-1):

%o ........dd.append((primes[x+1]%9) - (primes[x]%9))

%o ....return dd

%Y Cf. A000040, A010888.

%K base,sign,easy

%O 1,2

%A _Conner L. Delahanty_, Apr 18 2014