A234433
Primes which are the arithmetic mean of the cubes of three consecutive primes.
Original entry on oeis.org
3659642149, 7045360877, 13980508481, 43207190581, 55176987287, 67967949209, 85126672391, 146447402879, 263994755239, 296875570279, 344620720019, 382820725229, 400485072139, 476566488179, 527319634151, 663284454649
Offset: 1
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.
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.
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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);
A234469
Primes which are the arithmetic mean of the cubes of four consecutive primes.
Original entry on oeis.org
2077681, 16244203, 904456921, 2500135411, 2762662109, 10064833601, 65794585811, 122098559279, 144790176847, 245198071093, 268215631223, 2038246966633, 2782403547799, 3022844332973, 3593531892947
Offset: 1
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.
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.
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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);
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Select[Mean/@Partition[Prime[Range[2000]]^3,4,1],PrimeQ] (* Harvey P. Dale, Oct 12 2020 *)
Showing 1-2 of 2 results.