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A240278 Primes p which are floor of Root-Mean-Square (RMS) of prime(n), prime(n+1) and prime(n+2).

%I A240278 #12 Mar 23 2018 16:33:27
%S A240278 3,5,13,19,43,47,53,83,89,103,109,131,157,167,173,193,211,229,233,257,
%T A240278 263,313,349,353,359,373,383,389,409,443,449,463,503,563,593,607,643,
%U A240278 647,653,677,683,691,709,733,797,823,859,883,919,941,947,971,977,983,1013
%N A240278 Primes p which are floor of Root-Mean-Square (RMS) of prime(n), prime(n+1) and prime(n+2).
%H A240278 K. D. Bajpai, <a href="/A240278/b240278.txt">Table of n, a(n) for n = 1..3075</a>
%e A240278 11, 13 and 17 are consecutive primes: sqrt(( 11^2 + 13^2 + 17^2)/3) = 13.89244399: floor(13.89244399) = 13, which is prime and appears in the sequence.
%e A240278 17, 19 and 23 are consecutive  primes: sqrt(( 17^2 + 19^2 + 23^2)/3) = 19.82422760: floor(19.82422760) = 19, which is prime and appears in the sequence.
%e A240278 41, 43 and 47 are consecutive  primes: sqrt(( 41^2 + 43^2 + 47^2)/3) = 43.73785546: floor(43.73785546) = 43, which is prime and appears in the sequence.
%p A240278 a := proc(n) local c, b, d, e; c:=ithprime(n); b:=ithprime(n+1); d:=ithprime(n+2); e:=floor(sqrt((c^2+b^2+d^2)/3)); if isprime(e) then RETURN(e); fi; end: seq(a(n), n=1..500);
%t A240278 Select[Floor[RootMeanSquare[#]]&/@Partition[Prime[Range[200]],3,1],PrimeQ] (* _Harvey P. Dale_, Mar 23 2018 *)
%Y A240278 Cf. A000040, A075471, A088165.
%K A240278 nonn
%O A240278 1,1
%A A240278 _K. D. Bajpai_, Apr 03 2014