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A234469 Primes which are the arithmetic mean of the cubes of four consecutive primes. 1

%I #16 Oct 12 2020 19:15:32

%S 2077681,16244203,904456921,2500135411,2762662109,10064833601,

%T 65794585811,122098559279,144790176847,245198071093,268215631223,

%U 2038246966633,2782403547799,3022844332973,3593531892947

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

%H K. D. Bajpai, <a href="/A234469/b234469.txt">Table of n, a(n) for n = 1..3810</a>

%e 2077681 is in the sequence because (113^3 + 127^3 + 131^3 + 137^3)/4 = 2077681 which is prime.

%e 16244203 is in the sequence because (241^3 + 251^3 + 257^3 + 263^3)/4 = 16244203 which is prime.

%p 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);

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

%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

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)