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

%I A233468 #38 Mar 25 2025 15:02:13
%S A233468 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 A233468 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 A233468 -7,6,-5,2,1,-4,4,2,-5,5,-3,1,2,-5,6
%N A233468 The digital root of prime(n+1) minus the digital root of prime(n).
%H A233468 Conner L. Delahanty, <a href="/A233468/b233468.txt">Table of n, a(n) for n = 1..20000</a>
%F A233468 a(n) = (prime(n+1) mod 9) - (prime(n) mod 9).
%F A233468 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 A233468 a(n) = A010888(A000040(n+1)) - A010888(A000040(n)). - _Michel Marcus_, Apr 19 2014
%e A233468 For n = 1, (prime(2) mod 9) - (prime(1) mod 9) =  3 (mod 9) - 2 (mod 9) = 3-2 = 1.
%e A233468 For n = 2, (prime(3) mod 9) - (prime(2) mod 9) =  5 (mod 9) - 3 (mod 9) = 5-3 = 2.
%e A233468 For n = 3, (prime(4) mod 9) - (prime(3) mod 9) =  7 (mod 9) - 5 (mod 9) = 7-5 = 2.
%e A233468 For n = 4, (prime(5) mod 9) - (prime(4) mod 9) = 11 (mod 9) - 7 (mod 9) = 2-7 = -5.
%p A233468 A233468:=n->(ithprime(n+1) mod 9) - (ithprime(n) mod 9); seq(A233468(n), n=1..100); # _Wesley Ivan Hurt_, Apr 19 2014
%t A233468 Table[Mod[Prime[n + 1], 9] - Mod[Prime[n], 9], {n, 100}] (* _Wesley Ivan Hurt_, Apr 19 2014 *)
%o A233468 (Python)
%o A233468 dd=[]
%o A233468 def prim(end):
%o A233468     num=3
%o A233468     primes=[2, 3]
%o A233468     while (len(primes)<=end):
%o A233468         num+=1
%o A233468         prime=False
%o A233468         length=len(primes)
%o A233468         for y in range(0, length):
%o A233468             if (num % primes[y]!=0):
%o A233468                 prime=True
%o A233468             else:
%o A233468                 prime=False
%o A233468                 break
%o A233468         if (prime):
%o A233468             primes.append(num)
%o A233468     for x in range(len(primes)-1):
%o A233468         dd.append((primes[x+1]%9) - (primes[x]%9))
%o A233468     return dd
%Y A233468 Cf. A000040, A010888.
%K A233468 base,sign,easy
%O A233468 1,2
%A A233468 _Conner L. Delahanty_, Apr 18 2014