|
%I #12 Dec 27 2013 02:55:49
%S 3659642149,7045360877,13980508481,43207190581,55176987287,
%T 67967949209,85126672391,146447402879,263994755239,296875570279,
%U 344620720019,382820725229,400485072139,476566488179,527319634151,663284454649
%N Primes which are the arithmetic mean of the cubes of three consecutive primes.
%H K. D. Bajpai, <a href="/A234433/b234433.txt">Table of n, a(n) for n = 1..7100</a>
%e 3659642149 is in the sequence because (1531^3 + 1543^3 + 1549^3)/3 = 3659642149 which is prime.
%e 7045360877 is in the sequence because (1907^3 + 1913^3+ 1931^3)/3 = 7045360877 which is prime.
%p KD := proc() local a,b,d,e,f,g; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); g:=(a^3+b^3+d^3)/3; if g=floor(g) and isprime(g) then RETURN (g); fi; end: seq(KD(), n=2..2000);
%Y Cf. A084951: primes of the form (prime(k)^2 + prime(k+1)^2 + prime(k+2)^2)/3.
%Y Cf. A093343: primes of the form (prime(k)^2 + prime(k+1)^2)/2.
%Y Cf. A234358: cubes which are the arithmetic mean of four consecutive primes.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Dec 26 2013
| 