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Smallest prime greater than n*(n+1)^2/2.
1

%I #12 Aug 03 2014 14:01:26

%S 2,3,11,29,53,97,149,227,331,457,607,797,1019,1277,1579,1931,2333,

%T 2767,3251,3803,4421,5087,5821,6637,7507,8461,9479,10589,11777,13063,

%U 14419,15877,17431,19079,20849,22691,24659,26717,28901,31219,33623,36187,38833,41627

%N Smallest prime greater than n*(n+1)^2/2.

%H Charles R Greathouse IV, <a href="/A181956/b181956.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ n^3 / 2. - _Charles R Greathouse IV_, Aug 03 2012

%e a(1)=2 because prime 2 > (0*(0+1)^2/2) = 0, a(2)=3 because prime 3 > (1*(1+1)^2/2) = 2, a(3)=11 because prime 11 > (2*(2+1)^2/2) = 9.

%t Table[NextPrime[n*(n+1)^2/2], {n, 0, 50}] (* _T. D. Noe_, Apr 03 2012 *)

%o (PARI) a(n)=nextprime(n*(n+1)^2/2+1) \\ _Charles R Greathouse IV_, Aug 03 2012

%Y Cf. A006002, A097050.

%K nonn

%O 0,1

%A _Gerasimov Sergey_, Apr 03 2012