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Search: id:A106108
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| A106108 |
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a(1) = 7; for n >1, a(n) = a(n-1) + gcd(n, a(n-1)). |
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+0
14
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| 7, 8, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 141, 144, 145, 150, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The title refers to the sequence of first differences, A132199.
Setting a(1) = 4 gives A084662.
Rowland proves that the first differences are all 1's or primes. The prime differences form A137613.
See A137613 for additional comments, links, and references. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 14 2008]
"This recurrence was discovered at the 2003 NKS Summer School by a group led by Matt Frank. This Demonstration allows initial conditions . a(1) >= 4. For 1 =< a(1) =< 3, a(n) - a(n-1) is 1 for n >= 3." See Wolfram hyperlink. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 10 2008]
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REFERENCES
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Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric S. Rowland, A simple prime-generating recurrence.
Wolfram Demonstrations Project, Prime-Generating Recurrence. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 10 2008]
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MAPLE
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S:=7; f:= proc(n) option remember; global S; if n=1 then RETURN(S); else RETURN(f(n-1)+gcd(n, f(n-1))); fi; end; [seq(f(n), n=1..200)];
a[1] = 7; a[n_] := a[n] = a[n - 1] + GCD[n, a[n - 1]]; Array[a, 66] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 10 2008]
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CROSSREFS
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Cf. A084662, A084663, A132199, A134734, A134736, A134743, A134744, A134162, A137613.
Adjacent sequences: A106105 A106106 A106107 this_sequence A106109 A106110 A106111
Sequence in context: A035703 A065976 A120200 this_sequence A120309 A035705 A097338
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KEYWORD
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nonn,new
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AUTHOR
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njas, Jan 28 2008
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