A258934 - OEIS

%I #17 Sep 08 2022 08:46:13

%S 2,4,6,9,12,13,17,19,21,24,26,30,32,33,39,40,45,48,51,54,57,58,67,66,

%T 69,74,78,81,84,83,90,90,99,100,104,108,110,115,118,121,126,126,132,

%U 133,140,140,140,147,156,162,165,168,171,172,175,175,185,185,189

%N Half the difference between the 2n-th prime and the n-th prime, starting from n=2.

%C The differences between odd prime numbers are always even, so a(n) is well defined for n>=2.

%H Seiichi Manyama, <a href="/A258934/b258934.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = ( prime(2*n) - prime(n) ) / 2.

%F a(n) = A072473(n)/2.

%t Table[(Prime[2 k] - Prime[k])/2, {k, 2, 60}]

%o (Sage) [(nth_prime(2*n)-nth_prime(n))/2 for n in (2..60)] # _Bruno Berselli_, Jun 15 2015

%o (Magma) [(NthPrime(2*n)-NthPrime(n))/2: n in [2..60]]; // _Bruno Berselli_, Jun 15 2015

%Y Cf. A072473, A072715, A087461.

%K nonn,easy

%O 2,1

%A _Federico Provvedi_, Jun 15 2015