A114834 - OEIS

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A114834

Each term is previous term plus floor of root mean square of two previous terms.

1, 2, 3, 5, 9, 16, 28, 50, 90, 162, 293, 529 (list; graph; refs; listen; history; 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.`
	CROSSREFS	`Cf. A065094, A065095.` `Sequence in context: A099529 A088352 A002572 * A143961 A128023 A056303` `Adjacent sequences: A114831 A114832 A114833 * A114835 A114836 A114837`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006`

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Last modified February 17 06:27 EST 2012. Contains 205998 sequences.