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A137417
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Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value a(n).
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11
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1, 3, 3, 4, 8, 9, 7, 12, 9, 10, 11, 12, 21, 21, 24, 16, 17, 27, 19, 42, 21, 33, 23, 36, 25, 26, 27, 28, 29, 30, 31, 48, 33, 72, 56, 36, 37, 57, 63, 40, 41, 63, 43, 44, 72, 69, 47, 48, 49, 75, 51, 78, 53, 81, 88, 84, 57, 87, 59, 126, 61, 135, 63, 64, 65, 99, 67, 68, 69, 70, 71
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OFFSET
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1,2
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COMMENTS
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At the vast majority of positions the term is changed at most once, but at some positions a change occurs twice. An example is position 20. In step 4 the term at position 4 + a(4) = 8 is changed to 8 + a(4) = 12; in step 8 the term at position 8 + a(8) = 20 is changed to 20 + a(8) = 32; in step 10 the term at position 10 + a(10) = 20 is changed to a(20) + a(10) = 32 + 10 = 42.
The first position where the term is changed three times is 3498. [Klaus Brockhaus, Apr 23 2008]
The first position where the term is changed four times is 1024914. [Rémy Sigrist, Mar 11 2017]
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of first 2000000 terms
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MAPLE
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P:=proc(i) local a, n, v; v:=array(1..i); for n from 1 by 1 to i do v[n]:=n; od; for n from 1 by 1 to 200 do v[v[n]+n]:=v[v[n]+n]+v[n]; od; for n from 1 by 1 to 200 do print(v[n]); od; end: P(1000); # Paolo P. Lava, Mar 10 2009
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MATHEMATICA
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Block[{a, nn = 71}, a = Range[Max[3, IntegerLength[nn]] nn]; Do[a[[n + a[[n]]]] = a[[n + a[[n]]]] + a[[n]], {n, nn}]; a[[1 ;; nn]] ] (* Michael De Vlieger, Jul 28 2021 *)
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CROSSREFS
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Cf. A000027.
Sequence in context: A340429 A147679 A339054 * A137418 A357306 A285445
Adjacent sequences: A137414 A137415 A137416 * A137418 A137419 A137420
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka, Apr 16 2008
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EXTENSIONS
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Extended by Klaus Brockhaus, Apr 23 2008
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STATUS
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approved
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