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Search: id:A064550
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| A064550 |
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Define Hofstadter's batrachian Q-sequence (A005185) by Q(0) = Q(1) = 1, Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), n > 1; then a(1) = 2, a(n)=a(n-1)+2*Q(n)-n, n > 1. |
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+0
3
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| 1, 2, 4, 7, 9, 12, 16, 19, 23, 26, 28, 33, 37, 40, 46, 49, 53, 58, 62, 67, 71, 74, 76, 85, 89, 92, 98, 103, 107, 110, 120, 123, 125, 132, 140, 143, 147, 154, 158, 163, 169, 174, 180, 185, 189, 192, 194, 211, 211, 212, 222, 227, 227, 234, 240, 241
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Prime-like simulation using Hofstadter's Batrachian sequence as difference generator.
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REFERENCES
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Simone Caramel, personal communication, also postings to newsgroups.
Clifford Pickover, article on the crying of Batrachian sequences
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LINKS
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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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MAPLE
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A064550 := proc(n) option remember; if n=0 then 1 else A064550(n-1)+2*A005185(n-1)(n) - n; fi; end;
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MATHEMATICA
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q[0] = q[1] = 1; q[n_] := q[n - q[n - 1]] + q[n - q[n - 2]]; a[1] = 2; a[n_] := a[n] = a[n - 1] + 2*(q[n] - n/2); Table[ a[n], {n, 1, 70} ]
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PROGRAM
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(ARIBAS): function a064550(maxarg: integer); var n, r, rm, q: integer; qar: array; begin qar := alloc(array, maxarg + 1); qar[0] := 1; for n := 1 to maxarg do if n < 2 then q := 1; else q := qar[n - qar[n - 1]] + qar[n - qar[n - 2]]; end; qar[n] := q; if n = 1 then r := 2; else r := rm + round(2*(q - n/2)); end; rm := r; write(r, " "); end; end; a064550(65).
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CROSSREFS
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Cf. A064551, A064552, A005185.
Sequence in context: A065560 A134886 A024193 this_sequence A064491 A120878 A137996
Adjacent sequences: A064547 A064548 A064549 this_sequence A064551 A064552 A064553
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 08 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Matthew M. Conroy, Oct 09 2001
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