A230329 Prime(prime(2*n)) - 2*prime(n).

1, 11, 31, 53, 87, 131, 157, 203, 237, 295, 339, 387, 465, 501, 523, 633, 679, 755, 833, 889, 941, 1013, 1051, 1231, 1253, 1297, 1391, 1455, 1523, 1597, 1659, 1801, 1825, 1991, 2053, 2115, 2235, 2321, 2385, 2457, 2551, 2657, 2727, 2843, 2905

Offset: 1

Author

Gerasimov Sergey, Oct 16 2013

Keywords

• nonn
• easy

Comments

For n = 12239, 24046, 24140, 24255, ... a(n+1) = a(n), and for n = 2154, 2524, 2810, 3795, ... a(n+1) < a(n). What is the smallest number n such that a(n+2) <= a(n+1) <= a(n)? - Farideh Firoozbakht, Oct 18 2013

Using the Prime Number Theorem, prime(n) ~ n log n, the asymptotic behavior is the same as that of A217622, a(n) ~ 2n (log 2n) log(2n log 2n). - M. F. Hasler, Oct 19 2013

Crossrefs

Cf. A230098, A230285, A066066.

Programs

Mathematica

Table[Prime[Prime[2n]] - 2Prime[n], {n, 45}]

PARI

A230329(n)=prime(prime(2*n))-2*prime(n) \\ M. F. Hasler, Oct 19 2013

Formula

a(n) = A217622(n) - 2*A000040(n).

a(n) = A217622(n) - A100484(n). - Omar E. Pol, Oct 19 2013

Extensions

Corrected by R. J. Mathar, Oct 18 2013