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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)