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

3, 5, 13, 19, 43, 47, 53, 83, 89, 103, 109, 131, 157, 167, 173, 193, 211, 229, 233, 257, 263, 313, 349, 353, 359, 373, 383, 389, 409, 443, 449, 463, 503, 563, 593, 607, 643, 647, 653, 677, 683, 691, 709, 733, 797, 823, 859, 883, 919, 941, 947, 971, 977, 983, 1013

Offset: 1

Author

K. D. Bajpai, Apr 03 2014

Keywords

• nonn

Examples

			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.
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.
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.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3075

Crossrefs

Cf. A000040, A075471, A088165.

Programs

Maple

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);

Mathematica

Select[Floor[RootMeanSquare[#]]&/@Partition[Prime[Range[200]],3,1],PrimeQ] (* Harvey P. Dale, Mar 23 2018 *)