A024700 a(n) = (prime(n+2)^2 - 1)/3.

8, 16, 40, 56, 96, 120, 176, 280, 320, 456, 560, 616, 736, 936, 1160, 1240, 1496, 1680, 1776, 2080, 2296, 2640, 3136, 3400, 3536, 3816, 3960, 4256, 5376, 5720, 6256, 6440, 7400, 7600, 8216, 8856, 9296, 9976, 10680, 10920, 12160, 12416, 12936, 13200, 14840, 16576, 17176

Offset: 1

Author

Clark Kimberling, Dec 11 1999

Keywords

• nonn

Comments

Numbers of the form 4*h*(3*h +- 1). - Vincenzo Librandi, May 21 2013

This sequence is also: Numbers n such that k is prime and its square is of the form 3*n + 1 (i.e., k^2 = 3*n + 1). For this case, the sequence is to be prepended with a(0) = 1. - G. C. Greubel, Sep 18 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040 (prime(n)), A001248, A024701, A024702, A061066, A081115, A084920, A084921, A084922.

Programs

Magma

[(NthPrime(n+2)^2-1)/3: n in [1..50]]; // Bruno Berselli, May 22 2013

Mathematica

Select[Range[2,10000], PrimeQ[Sqrt[3*#+1]] &] (* G. C. Greubel, Sep 18 2016 *)
(Prime[Range[3,50]]^2-1)/3 (* Harvey P. Dale, May 05 2022 *)

PARI

a(n) = (prime(n+2)^2-1)/3; \\ Altug Alkan, Sep 18 2016

SageMath

[(n^2 -1)/3 for n in prime_range(4,301)] # G. C. Greubel, May 02 2024

Formula

a(n) = (A001248(n+2) - 1)/3. - Elmo R. Oliveira, Jan 20 2023

a(n) = 8*A024702(n+2) = 4*A081115(n+2) = 2*A084922(n+2) = (2/3)*A084921(n) = (4/3)*A024701(n+1) = (8/3)*A061066(n+2). - Alois P. Heinz, Jan 20 2023