A234433 Primes which are the arithmetic mean of the cubes of three consecutive primes.

3659642149, 7045360877, 13980508481, 43207190581, 55176987287, 67967949209, 85126672391, 146447402879, 263994755239, 296875570279, 344620720019, 382820725229, 400485072139, 476566488179, 527319634151, 663284454649

Offset: 1

Author

K. D. Bajpai, Dec 26 2013

Keywords

• nonn

Examples

			3659642149 is in the sequence because (1531^3 + 1543^3 + 1549^3)/3 = 3659642149 which is prime.
7045360877 is in the sequence because (1907^3 + 1913^3+  1931^3)/3 = 7045360877 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..7100

Crossrefs

Cf. A084951: primes of the form (prime(k)^2 + prime(k+1)^2 + prime(k+2)^2)/3.

Cf. A093343: primes of the form (prime(k)^2 + prime(k+1)^2)/2.

Cf. A234358: cubes which are the arithmetic mean of four consecutive primes.

Programs

Maple

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);