

A081115


(p^2  1)/12 where p > 3 runs through the primes.


3



2, 4, 10, 14, 24, 30, 44, 70, 80, 114, 140, 154, 184, 234, 290, 310, 374, 420, 444, 520, 574, 660, 784, 850, 884, 954, 990, 1064, 1344, 1430, 1564, 1610, 1850, 1900, 2054, 2214, 2324, 2494, 2670, 2730, 3040, 3104, 3234, 3300, 3710, 4144, 4294, 4370, 4524
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OFFSET

3,1


COMMENTS

If p=4k+1, (p^2  1)/12 = Sum_{i=1..k} floor(sqrt(i*k)) (see links).  R. J. Mathar, Jul 07 2006
For n=1 and 2, the corresponding primes being 2 and 3, and a(n) is a fraction, not entered here.  Michel Marcus, Nov 11 2013
For prime p > 3, (p^2  1)/12 = (1/p)*Sum_{k=0..floor(p/2)} (p  k)*k.  Joseph Wheat, Feb 03 2018


LINKS

Muniru A Asiru, Table of n, a(n) for n = 3..5000
Hojoo Lee, Problems in Elementary Number Theory, p. 14, problem 10.
George PĆ³lya and Gabor Szego, Problems and Theorems in Analysis II, p. 113, problem 20.
S. A. Shirali, A family portrait of primes  a case study in discrimination, Math. Mag.. Vol. 70, No. 4 (Oct. 1997), pp. 263272.


FORMULA

a(n) = j*(j+1)/3 where A000040(n)=2*j+1.  R. J. Mathar, Jul 07 2006
a(n) = (A001248(n)  1)/12.  Vicente Izquierdo Gomez, May 25 2013
a(n) = 2*A024702(n).  R. J. Mathar, Jan 09 2017


MAPLE

seq((ithprime(p)^21)/12, p=3..20); # Muniru A Asiru, Feb 04 2018


MATHEMATICA

(Prime[Range[3, 51]]^2  1)/12 (* Giovanni Resta, May 25 2013 *)


PROG

(PARI) a(n) = p = prime(n); (p^21)/12; \\ Michel Marcus, Nov 11 2013
(GAP) List(Filtered([5..20], IsPrime), p>(p^21)/12); # Muniru A Asiru, Feb 04 2018


CROSSREFS

Sequence in context: A139480 A227388 A152749 * A053417 A082230 A236547
Adjacent sequences: A081112 A081113 A081114 * A081116 A081117 A081118


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Apr 16 2003


EXTENSIONS

Offset set to 3 and edited by Michel Marcus, Nov 11 2013


STATUS

approved



