A258934 Half the difference between the 2n-th prime and the n-th prime, starting from n=2.

2, 4, 6, 9, 12, 13, 17, 19, 21, 24, 26, 30, 32, 33, 39, 40, 45, 48, 51, 54, 57, 58, 67, 66, 69, 74, 78, 81, 84, 83, 90, 90, 99, 100, 104, 108, 110, 115, 118, 121, 126, 126, 132, 133, 140, 140, 140, 147, 156, 162, 165, 168, 171, 172, 175, 175, 185, 185, 189

Offset: 2

Author

Federico Provvedi, Jun 15 2015

Keywords

• nonn
• easy

Comments

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A072473, A072715, A087461.

Programs

Magma

[(NthPrime(2*n)-NthPrime(n))/2: n in [2..60]]; // Bruno Berselli, Jun 15 2015

Mathematica

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

Sage

[(nth_prime(2*n)-nth_prime(n))/2 for n in (2..60)] # Bruno Berselli, Jun 15 2015

Formula

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

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