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Search: id:A079000
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| A079000 |
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a(n) is taken to be the smallest positive integer greater than a(n-1) which is consistent with the condition "n is a member of the sequence if and only if a(n) is odd". |
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61
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| 1, 4, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 97
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(a(n)) = 2n+3 for n>1.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..10000
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
N. J. A. Sloane, Seven Staggering Sequences.
Index entries for sequences of the a(a(n)) = 2n family
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FORMULA
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a(1) = 1, a(2) = 4, then a(9*2^k-3+j) = 12*2^k-3+3*j/2+|j|/2 for k>=0, -3*2^k <= j <= 3*2^k. Also a(3n) = 3*b(n/3), a(3n+1) = 2*b(n)+b(n+1), a(3n+2) = b(n)+2*b(n+1) for n>=2, where b = A079905. - njas and Ben Cloitre, Feb 20, 2003
a(n+1)-2*a(n)+a(n-1) = 1 for n=9*2^k-3, k>=0, = -1 for n = 2 and 3*2^k-3, k>=1, and = 0 otherwise.
a(n) = (3*n+3-3*2^g(n)+(-1)^f(n)*(9*2^g(n)-n-3))/2 for n>3, f(n)=A079944(A002264(n-4)) and g(n)=A000523(A002264(n+2)/2). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 23 2003
Also a(n) = n+3*2^A000523(A002264(n+2)/2)*(1-3*A080584(n-4))+A080584(n-4)*(n+3) for n>3, where A080584(n)=A079944(A002264(n)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 24 2003
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EXAMPLE
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a(2) cannot be 2 because 2 is even; it cannot be 3 because that would require 2 to be a member of the sequence. Hence a(2)=4, and the next odd member of the sequence is the fourth member.
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MAPLE
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Digits := 50; A079000 := proc(n) local k, j; if n<=2 then n^2; else k := floor(evalf(log( (n+3)/6 )/log(2)) ); j := n-(9*2^k-3); 12*2^k-3+3*j/2 +abs(j)/2; fi; end;
A002264 := n->floor(n/3): A079944 := n->floor(log[2](4*(n+2)/3))-floor(log[2](n+2)): A000523 := n->floor(log[2](n)): f := n->A079944(A002264(n-4)): g := n->A000523(A002264(n+2)/2): A079000 := proc(n) if n>3 then RETURN(simplify(3*n+3-3*2^g(n)+(-1)^f(n)*(9*2^g(n)-n-3))/2) else if n>0 then RETURN([1, 4, 6][n]) else RETURN(0) fi fi: end;
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CROSSREFS
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Cf. A079250-A079259, A079313, A079325, A064437, A003605, A079352, A079358.
Cf. also A080596, A080731, A080752.
Partial sums give A080566. Differences give A079948.
Sequence in context: A043860 A043869 A114308 this_sequence A047509 A105432 A139490
Adjacent sequences: A078997 A078998 A078999 this_sequence A079001 A079002 A079003
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Matthew Vandermast (ghodges14(AT)comcast.net), Feb 01 2003
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