cp's OEIS Frontend

A335139 a(n) = (prime(n + 1) +- k) / 2 where k is the smallest possible odd number such that a(n) is prime and a(n + 1) >= a(n).

%I A335139 #21 Sep 04 2020 15:55:19
%S A335139 2,3,3,5,7,7,11,11,13,17,19,19,23,23,29,29,31,31,37,37,41,41,43,47,53,
%T A335139 53,53,53,59,61,67,67,71,73,73,79,83,83,89,89,89,97,97,97,101,107,113,
%U A335139 113,113,113,113,127,127,127,131,137,137,139,139,139,149
%N A335139 a(n) = (prime(n + 1) +- k) / 2 where k is the smallest possible odd number such that a(n) is prime and a(n + 1) >= a(n).
%C A335139 The sequence of k's begins {1, 1, -1, -1, 1, -3, 3, -1, -3, 3, 1, -3, 3, -1, ...}. I conjecture that the partial sums of the k's sequence change sign infinitely often and that their absolute value is less than the square root of n.
%o A335139 (PARI) forprime(n = 3, 300, forstep(j = 1, 999, 2, a = (n + j)/2; b =(n - j)/2; if(isprime(a), print1(a", "); break); if(isprime(b), print1(b", "); break)))
%Y A335139 Cf. A000040.
%K A335139 nonn
%O A335139 1,1
%A A335139 _Dimitris Valianatos_, May 24 2020