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A019444
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a_1, a_2, ..., is a permutation of the positive integers such that the average of each initial segment is an integer, using the greedy algorithm to define a_n.
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6
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1, 3, 2, 6, 8, 4, 11, 5, 14, 16, 7, 19, 21, 9, 24, 10, 27, 29, 12, 32, 13, 35, 37, 15, 40, 42, 17, 45, 18, 48, 50, 20, 53, 55, 22, 58, 23, 61, 63, 25, 66, 26, 69, 71, 28, 74, 76, 30, 79, 31, 82, 84, 33, 87, 34, 90, 92, 36, 95, 97, 38, 100, 39, 103, 105, 41, 108, 110, 43, 113
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Self-inverse when considered as a permutation or function, i.e. a(a(n)) = n. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
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LINKS
| Franklin T. Adams-Watters, Table of n, a(n) for n=1..10000
Problem of the week, Web site - problem 818
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| Let s(n) = sum(k=1,n,a(k))/n = A019446(n). Then if s(n-1) does not occur in a(1),...,a(n-1), a(n) = s(n) = s(n-1); otherwise, a(n) = s(n-1) + n and s(n) = s(n-1) + 1. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 20 2010]
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MATHEMATICA
| a[1]=1; a[n_] := a[n]=Module[{s, v}, s=a/@Range[n-1]; For[v=Mod[ -Plus@@s, n], v<1||MemberQ[s, v], v+=n, Null]; v]
lst = {1}; f[s_List] := Block[{k = 1, len = 1 + Length@ lst, t = Plus @@ lst}, While[ MemberQ[s, k] || Mod[k + t, len] != 0, k++ ]; AppendTo[lst, k]]; Nest[f, lst, 69] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 17 2010]
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PROG
| (PARI) al(n)=local(v, s, fnd); v=vector(n); v[1]=s=1; for(k=2, n, fnd=0; for(i=1, k-1, if(v[i]==s, fnd=1; break)); v[k]=if(fnd, s+k, s); s+=fnd); v [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 20 2010]
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CROSSREFS
| Cf. A019445, A019446. A019444 = A002251 + 1.
Sequence in context: A193998 A160855 A120232 * A195412 A069773 A122321
Adjacent sequences: A019441 A019442 A019443 * A019445 A019446 A019447
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KEYWORD
| nonn,nice
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AUTHOR
| R. K. Guy and Tom Halverson (halverson(AT)macalester.edu)
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