A234469 Primes which are the arithmetic mean of the cubes of four consecutive primes.

2077681, 16244203, 904456921, 2500135411, 2762662109, 10064833601, 65794585811, 122098559279, 144790176847, 245198071093, 268215631223, 2038246966633, 2782403547799, 3022844332973, 3593531892947

Offset: 1

Author

K. D. Bajpai, Dec 26 2013

Keywords

• nonn

Examples

			2077681 is in the sequence because (113^3 + 127^3 + 131^3 + 137^3)/4 = 2077681 which is prime.
16244203 is in the sequence because (241^3 + 251^3 + 257^3 + 263^3)/4 = 16244203 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3810

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,g; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=ithprime(n+3); g:=(a^3+b^3+d^3+e^3)/4; if g=floor(g) and isprime(g) then RETURN (g); fi; end: seq(KD(), n=1..5000);

Mathematica

Select[Mean/@Partition[Prime[Range[2000]]^3,4,1],PrimeQ] (* Harvey P. Dale, Oct 12 2020 *)