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Search: id:A004793
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| A004793 |
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a(1)=1, a(2)=3; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression. |
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11
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| 1, 3, 4, 6, 10, 12, 13, 15, 28, 30, 31, 33, 37, 39, 40, 42, 82, 84, 85, 87, 91, 93, 94, 96, 109, 111, 112, 114, 118, 120, 121, 123, 244, 246, 247, 249, 253, 255, 256, 258, 271, 273, 274, 276, 280, 282, 283, 285, 325, 327, 328, 330, 334, 336, 337, 339, 352, 354
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Iacobescu, F. 'Smarandache Partition Type and Other Sequences.' Bull. Pure Appl. Sci. 16E, 237-240, 1997.
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = (3-n)/2 + 2*floor(n/2) + sum(k=1, n-1, 3^A007814(k))/2 = A003278(n) + [n is even], proved by Lawrence Sze, following a conjecture by Ralf Stephan.
a(n) = b(n-1), with b(0)=1, b(2n)=3b(n)-2-3[n odd], b(2n+1)=3b(n)-3[n odd].
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PROGRAM
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(PARI) v[1]=1:v[2]=3:for(n=3, 1000, f=2:m=v[n-1]+1:while(1, forstep(k=n-1, 1, -1, if(v[k]<(m+1)/2, f=1:break):for(l=1, k-1, if(m-v[k]==v[k]-v[l], f=0:break)): if(f<2, break)): if(!f, m=m+1:f=2): if(f==1, break)):v[n]=m) (Ralf Stephan)
(PARI) a(n)=if(n<1, 1, if(n%2==0, 3*a(n/2)-2-3*((n/2)%2), 3*a((n-1)/2)-3*(((n-1)/2)%2))) (Ralf Stephan)
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CROSSREFS
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Cf. A092482.
Row 1 of array in A093682.
Sequence in context: A047296 A137951 A082694 this_sequence A031132 A057477 A113887
Adjacent sequences: A004790 A004791 A004792 this_sequence A004794 A004795 A004796
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Rechecked by David W. Wilson, Jun 04, 2002.
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