A098764 a(n) = 3p - q where p and q are consecutive primes.

3, 4, 8, 10, 20, 22, 32, 34, 40, 56, 56, 70, 80, 82, 88, 100, 116, 116, 130, 140, 140, 154, 160, 170, 190, 200, 202, 212, 214, 212, 250, 256, 272, 268, 296, 296, 308, 322, 328, 340, 356, 352, 380, 382, 392, 386, 410, 442, 452, 454, 460, 476, 472, 496, 508, 520

Offset: 1

Author

Giovanni Teofilatto, Sep 30 2004

Keywords

• nonn
• easy

Comments

Except for the initial term, a(n)=={2, 4} mod 6.

Not monotonic: a(29) = 214 > 212 = a(30), a(33) = 272 > 268 = a(34), etc. - Charles R Greathouse IV, Jun 03 2013

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001043, A001223, A001748, A047235, A100021.

Programs

Mathematica

ListConvolve[{-1,3},Prime[Range[100]]] (* Paolo Xausa, Nov 02 2023 *)

PARI

a(n) = 3*prime(n) - prime(n+1) \\ Michel Marcus, Jun 03 2013

Formula

a(n) = A001043(n) - 2*A001223(n).

a(n) = 3*A000040(n)-A000040(n+1) = A001748(n)-A000040(n+1) = A001747(n+1)-A001223(n). - R. J. Mathar, Apr 22 2010

a(n) ~ 2n log n. - Charles R Greathouse IV, Jun 03 2013

a(n) = A100021(n) + 3. - Hugo Pfoertner, Nov 02 2023

a(n) = A062234(n) + A000040(n). - Anthony S. Wright, Feb 19 2024

Extensions

Corrected (116 duplicated) by R. J. Mathar, Apr 22 2010