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A234318 Squares t^2 = (p+q+r+s)/4 which are the arithmetic mean of four consecutive primes such that p < t^2 < q < r < s. 1
15876, 35721, 59049, 65025, 488601, 828100, 1144900, 3857296, 4822416, 4901796, 5107600, 5322249, 5856400, 6100900, 6760000, 10536516, 11716929, 12503296, 13468900, 14197824, 14638276, 15163236, 18748900, 21455424, 22127616, 22638564, 24049216, 24098281, 24108100 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..2869

EXAMPLE

15876 is in the sequence because 15876 = 126^2 = (15859+15877+15881+15887)/4, that is arithmetic mean of four consecutive primes.

35721 is in the sequence because 35721 = 189^2 = (35677+35729+35731+35747)/4, that is arithmetic mean of four consecutive primes.

MAPLE

KD := proc() local a, b, d, e, f, g; a:=n^2; b:=prevprime(a); d:=nextprime(a); e:=nextprime(d); f:=nextprime(e); g:=(b+d+e+f)/4; if a=g then RETURN (a); fi; end: seq(KD(), n=2..10000);

MATHEMATICA

fcpQ[{a_, b_, c_, d_}]:=Module[{m=Mean[{a, b, c, d}]}, IntegerQ[ Sqrt[ m]] && a< m< b]; Mean/@Select[Partition[Prime[Range[1600000]], 4, 1], fcpQ] (* Harvey P. Dale, Apr 24 2017 *)

PROG

(PARI) list(lim)=my(v=List(), p=2, q=3, r=5, t); forprime(s=7, nextprime(nextprime(lim+1)+1), t=(p+q+r+s)/4; if(denominator(t)==1 && issquare(t) && t < q, listput(v, t)); p=q; q=r; r=s); Vec(v) \\ Charles R Greathouse IV, Jan 03 2014

CROSSREFS

Cf. A000290 (squares:  a(n) = n^2).

Cf. A062703 (squares: sum of two consecutive primes).

Cf. A069495 (squares: arithmetic mean of two consecutive primes).

Cf. A234240 (cubes: arithmetic mean of three consecutive primes).

Cf. A234297 (squares: arithmetic mean of three consecutive primes).

Sequence in context: A277350 A101320 A031811 * A174596 A237071 A251848

Adjacent sequences:  A234315 A234316 A234317 * A234319 A234320 A234321

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Dec 23 2013

EXTENSIONS

Definition corrected by Michel Marcus and Charles R Greathouse IV, Jan 03 2014

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)