cp's OEIS Frontend

A235431 The smallest positive number that must be added to or subtracted from the sum of the first n primes in order to get a prime.

%I A235431 #45 May 11 2025 23:48:01
%S A235431 1,2,1,2,1,2,1,2,1,2,3,2,1,2,3,2,1,2,1,2,3,4,3,4,1,2,5,2,1,4,1,4,1,2,
%T A235431 3,4,5,2,3,2,5,2,1,2,1,2,3,2,1,2,1,2,3,2,1,2,1,10,1,4,11,2,1,6
%N A235431 The smallest positive number that must be added to or subtracted from the sum of the first n primes in order to get a prime.
%C A235431 The primes in A013918 would have associated a(n)=0 if not for the qualifier "positive" in the definition.
%C A235431 The sum of the first n primes appears to be close to a prime. For illustration, the maximum for a(n) among the first 5 million terms is a(808500) = 218.
%C A235431 See A013916 for the above mentioned indices, numbers n such that the sum of the first n primes is prime. - _M. F. Hasler_, Jan 20 2014
%H A235431 R. J. Cano, <a href="/A235431/b235431.txt">Table of n, a(n) for n = 1..10000</a>
%F A235431 Algorithm:
%F A235431 Let S be the sum of the first n primes;
%F A235431 initially, let k=1;
%F A235431 increment k while neither S-k nor S+k is prime;
%F A235431 return a(n)=k.
%F A235431 a(n) = min(A013632(A007504(n)), A049711(A007504(n))). - _M. F. Hasler_, Jan 20 2014
%e A235431 The sum of the first 9 primes is 100, and by adding 1 we get 101. Since 101 is a prime, a(9) = 1.
%e A235431 The sum of the first 10 primes is 129, since 129 - 2 = prime(31) = 127 or 129 + 2 = prime(32) = 131, a(10) = 2.
%e A235431 The sum of the first 129 primes minus 1 is a prime, this is 42468 - 1 = prime(4443), so a(129) = 1.
%o A235431 (PARI) a(n)=my(u=sum(j=1,n,prime(j)),k=1);while(!(isprime(u+k)||isprime(u-k)),k++);k
%Y A235431 Cf. A007504, A101301.
%K A235431 nonn,easy,hear
%O A235431 1,2
%A A235431 _R. J. Cano_, Jan 17 2014