A234539 Pentagonal numbers P = (p+q+r+s)/3 which are the arithmetic mean of four consecutive primes such that p < P < q < r < s.

852, 172212, 272001, 341055, 777240, 1451892, 1710402, 2361910, 2922526, 3950382, 4794522, 5414050, 6272015, 7989142, 10580176, 10780301, 11325882, 12173777, 12483395, 14432055, 14665630, 15890910, 16581775, 16962972, 17124772

Offset

1,1

Comments

The n-th pentagonal number is (3*n^2 - n)/2 = n*(3*n - 1)/2.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1786

Example

852 is in the sequence because 852 = 24*(3*24-1)/2 = (839 + 853 + 857 + 859)/4, the arithmetic mean of four consecutive primes.
172212 is in the sequence because 172212 = 339*(3*339-1)/2 = (172199 +172213+ 172217 + 172219)/4, the arithmetic mean of four consecutive primes.

Maple

KD := proc() local a, b, d, e, f, g; a:= n*(3*n-1)/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..5000);

Crossrefs

Cf. A000326 (pentagonal numbers: n*(3*n-1)/2).

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

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

Sequence in context: A237762 A237763 A237760 * A251148 A127593 A248856

Adjacent sequences: A234536 A234537 A234538 * A234540 A234541 A234542

Keyword

nonn,less

Author

K. D. Bajpai, Dec 27 2013

Status

approved