A256454 - OEIS

%I #19 May 03 2022 23:15:49

%S 2,3,7,23,89,139,199,293,1831,1913,3089,3229,4177,5531,5953,6491,

%T 10799,11743,12853,30593,33247,34981,36389,81463,86629,95651,103237,

%U 106033,153191,181303,189067,190409,288583,294563,326369,399283,507217,514967,570253,642281,815729,841459,979567

%N a(n) = smallest prime(j) > a(n-1) such that prime(j+1) - prime(j) = 2n, a(0) = 2.

%H Bill McEachen and Robert G. Wilson v, <a href="/A256454/b256454.txt">Table of n, a(n) for n = 0..180</a>

%F a(n) = A253899(n) - 2n for n > 0.

%e a(4) = 89 since 89=97-8, and this is the first time this gap is seen after smaller gaps of 1,2,4,6 are satisfied.

%t lst = {2}; p = 2; q = 3; gp = 2; While[ gp != 86, While[q - p != gp, p = q; q = NextPrime@ p]; AppendTo[lst, p]; Print@ p; gp += 2]; lst

%o (Python) from sympy import sieve

%o A256454 = [2]

%o for j in range(2,90000):

%o     if sieve[j+1] - sieve[j] == 2 * len(A256454): A256454.append(sieve[j])

%o print(A256454) # _Karl-Heinz Hofmann_, May 03 2022

%Y Cf. A000230, A000101, A253899 (upper end).

%K nonn

%O 0,1

%A _Bill McEachen_ and _Robert G. Wilson v_, Mar 29 2015