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a(n) = floor( sqrt( p * (p+2) / 2)) where p is the lesser of the twin primes.
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%I #10 Mar 08 2024 09:03:03

%S 2,4,8,12,21,29,42,50,72,76,97,106,127,135,140,161,169,190,199,220,

%T 246,296,305,326,369,403,424,436,453,466,572,581,585,606,623,721,729,

%U 742,750,772,814,869,903,912,920,933,1009,1026,1047,1052,1137,1145,1179

%N a(n) = floor( sqrt( p * (p+2) / 2)) where p is the lesser of the twin primes.

%H Harvey P. Dale, <a href="/A076651/b076651.txt">Table of n, a(n) for n = 1..1000</a>

%t a = Select[ Range[300], PrimeQ[ Prime[ # ] + 2] & ]; Floor[ Sqrt[ Prime[a]*Prime[a + 1]/2 ]]

%t Floor[Sqrt[Times@@#/2]]&/@Select[Partition[Prime[Range[500]],2,1],#[[2]] - #[[1]]==2&] (* _Harvey P. Dale_, Jun 13 2013 *)

%Y Cf. A001359.

%K nonn

%O 1,1

%A _Cino Hilliard_ and _Robert G. Wilson v_, Oct 20 2002