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 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 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

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