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A064552
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Define q(0)=1, q(1)=1, q(2)=1, q(3)=1, q(n)=q(abs(n-q(n-3)))+q(abs(n-q(n-4))) (A064657); then a(0) = 1, a(n)=a(n-1)+2*(q(n)-n/2), n > 0.
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4
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1, 2, 2, 1, 1, 4, 14, 31, 43, 44, 38, 31, 45, 56, 94, 105, 95, 96, 106, 109, 111, 140, 142, 171, 173, 174, 202, 229, 253, 232, 206, 187, 223, 210, 296, 271, 291, 360, 366, 451, 461, 468, 470, 477, 477, 534, 564, 567, 575, 532, 534, 589, 569, 622, 622, 693, 689, 640, 602, 567, 679
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A quadratic level Hofstadter batrachian sequence as a minimal type Pisot used in the prime simulation formula.
This quartic level Hofstadter sequence is set as a x^4-x-1=0 type Pisot with nonlinear index addressing. These work well at cubic levels as well to give Pickover numbers.
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LINKS
| Roger L. Bagula, A Simulation of a Prime Type of Sequence: The Hofstadter Integers
Matthew M. Conroy, Home page (listed instead of email address)
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MATHEMATICA
| a[0] = q[0] = q[1] = q[2] = q[3] = 1; q[n_] := q[n] = q[Abs[n - q[n - 3]]] + q[Abs[n - q[n - 4]]]; a[n_] := a[n] = a[n - 1] + 2*(q[n] - n/2); Table[a[n], {n, 0, 70} ]
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PROG
| (ARIBAS): function qfunc(n: integer): integer; var r: integer; begin if n < 4 then r := 1; else r := qfunc(abs(n - qfunc(n - 3))) + qfunc(abs(n - qfunc( n - 4))); end; return r; end; function a064552(n: integer); var k, r: integer; begin if n = 0 then r := 1; else r := a064552(n - 1) + round(2*(qfunc(n) - n/2)); end; return r; end; for n := 1 to 60 do write(a064552(n), " "); end; .
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CROSSREFS
| Cf. A064550, A064551, A064657.
Sequence in context: A176663 A113021 A152937 * A178655 A178304 A123585
Adjacent sequences: A064549 A064550 A064551 * A064553 A064554 A064555
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 08 2001
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EXTENSIONS
| Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Matthew M. Conroy and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 09, 2001
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