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A234370 Primes which are the arithmetic mean of the squares of five consecutive primes. 1
2723401, 13036537, 52774873, 78972121, 116515177, 123179113, 235236049, 242120017, 834990721, 850037521, 943067353, 943804801, 1302156313, 1582432681, 1659047497, 1830419449, 1999538809, 2025774697, 2609800657 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
2723401 is in the sequence because (1627^2 + 1637^2 + 1657^2 + 1663^2 + 1667^2)/5 = 2723401 which is prime.
52774873 is in the sequence because (7243^2 + 7247^2 + 7253^2 + 7283^2 + 7297^2)/5 = 52774873 which is prime.
MAPLE
KD := proc() local a, b, d, e, f, g; a:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=ithprime(n+3); f:=ithprime(n+4); g:=(a^2+b^2+d^2+e^2+f^2)/5; if g=floor(g) and isprime(g) then RETURN (g); fi; end: seq(KD(), n=1..10000);
MATHEMATICA
Select[Mean/@Partition[Prime[Range[6000]]^2, 5, 1], PrimeQ] (* Harvey P. Dale, Aug 01 2020 *)
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.
Sequence in context: A081409 A251997 A104848 * A051384 A251350 A238070
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Dec 25 2013
STATUS
approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)