login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A114834 Each term is previous term plus floor of root mean square of two previous terms. 1
1, 2, 3, 5, 9, 16, 28, 50, 90, 162, 293, 529, 956, 1728, 3124, 5648, 10211, 18462, 33380, 60352, 109119, 197293, 356716, 644961, 1166123, 2108412, 3812120, 6892514, 12462029, 22532007, 40739059, 73658371, 133178227, 240793271, 435366958, 787166465 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

What is this sequence and the ratio of adjacent terms, asymptotically? Primes in this sequence include 2, 3, 5, 293. Squares in this sequence include 9, 16, 529.

LINKS

Table of n, a(n) for n=1..36.

Eric Weisstein's World of Mathematics, Root-Mean-Square.

Eric Weisstein's World of Mathematics, Mean.

FORMULA

a(1) = 1, a(2) = 2, for n>2: a(n+1) = a(n) + floor(RMS[a(n),a(n-1)]). a(n+1) = a(n) + floor[Sqrt[[a(n)^2]+[a(n-1)^2]/2]].

EXAMPLE

a(3) = 2 + floor[sqrt[(1^2 + 2^2)/2]] = 2 + floor[Sqrt[5/2]] = 2 + 1 = 3.

a(4) = 3 + floor[sqrt[(2^2 + 3^2)/2]] = 4 + floor[Sqrt[13/2]] = 3 + 2 = 5.

a(5) = 5 + floor[sqrt[(3^2 + 5^2)/2]] = 8 + floor[Sqrt[34/2]] = 5 + 4 = 9.

a(6) = 9 + floor[sqrt[(5^2 + 9^2)/2]] = 15 + floor[Sqrt[106/2]] = 9 + 7 = 16.

a(7) = 16 + floor[sqrt[(9^2 + 16^2)/2]] = 15 + floor[Sqrt[337/2]] = 16 + 12 = 28.

a(8) = 28 + floor[sqrt[(16^2 + 28^2)/2]] = 15 + floor[Sqrt[1040/2]] = 28 + 22 = 50.

a(9) = 50 + floor[sqrt[(28^2 + 50^2)/2]] = 50 + floor[Sqrt[3284/2]] = 50 + 40 = 90.

a(10) = 90 + floor[sqrt[(50^2 + 90^2)/2]] = 50 + floor[Sqrt[10600/2]] = 90 + 72 = 162.

a(11) = 162 + floor[sqrt[(90^2 + 162^2)/2]] = 50 + floor[Sqrt[34344/2]] = 162 + 131 = 293.

a(12) = 293 + floor[sqrt[(162^2 + 293^2)/2]] = 293 + floor[Sqrt[112093/2]] = 293 + 236 = 529.

MAPLE

rms := proc(a, b)

    sqrt((a^2+b^2)/2) ;

end proc:

A114834 := proc(n)

    option remember;

    if n<= 2 then

        n;

    else

        procname(n-1)+floor(rms(procname(n-1), procname(n-2))) ;

    end if;

end proc: # R. J. Mathar, Jun 23 2014

CROSSREFS

Cf. A065094, A065095.

Sequence in context: A099529 A088352 A002572 * A143961 A128023 A000048

Adjacent sequences:  A114831 A114832 A114833 * A114835 A114836 A114837

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 19 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 22 05:47 EDT 2019. Contains 325213 sequences. (Running on oeis4.)