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A024700 a(n) = (prime(n+2)^2 - 1)/3. 4

%I #55 May 02 2024 04:28:59

%S 8,16,40,56,96,120,176,280,320,456,560,616,736,936,1160,1240,1496,

%T 1680,1776,2080,2296,2640,3136,3400,3536,3816,3960,4256,5376,5720,

%U 6256,6440,7400,7600,8216,8856,9296,9976,10680,10920,12160,12416,12936,13200,14840,16576,17176

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

%C Numbers of the form 4*h*(3*h +- 1). - _Vincenzo Librandi_, May 21 2013

%C 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

%H Vincenzo Librandi, <a href="/A024700/b024700.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (A001248(n+2) - 1)/3. - _Elmo R. Oliveira_, Jan 20 2023

%F 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

%t Select[Range[2,10000], PrimeQ[Sqrt[3*#+1]] &] (* _G. C. Greubel_, Sep 18 2016 *)

%t (Prime[Range[3,50]]^2-1)/3 (* _Harvey P. Dale_, May 05 2022 *)

%o (Magma) [(NthPrime(n+2)^2-1)/3: n in [1..50]]; // _Bruno Berselli_, May 22 2013

%o (PARI) a(n) = (prime(n+2)^2-1)/3; \\ _Altug Alkan_, Sep 18 2016

%o (SageMath) [(n^2 -1)/3 for n in prime_range(4,301)] # _G. C. Greubel_, May 02 2024

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

%K nonn

%O 1,1

%A _Clark Kimberling_, Dec 11 1999

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Last modified May 31 19:57 EDT 2024. Contains 373003 sequences. (Running on oeis4.)