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Search: id:A140778
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| A140778 |
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a(n) is the smallest positive integer such that no number occurs twice in the sequence and its absolute first differences. |
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+0
3
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| 1, 3, 7, 12, 18, 8, 17, 28, 13, 27, 43, 19, 39, 60, 22, 45, 70, 26, 55, 85, 31, 63, 96, 34, 69, 105, 37, 77, 118, 42, 88, 135, 48, 97, 147, 52, 103, 156, 56, 113, 171, 59, 120, 184, 65, 131, 198, 71, 143, 216, 74, 149, 227, 79, 159, 240, 82, 165, 249, 86, 175, 265, 91, 183
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence and its first differences include every positive integer (exactly once).
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EXAMPLE
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For a(5), the sequence to that point is [1,3,7,12], with absolute differences [2,4,5]. The next number cannot be 6, because then 6 would be in both the sequence and the first differences. Since all values smaller than 6 are taken, the difference must be positive and at least 6. A difference of 6 works, a(5) = 18.
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PROGRAM
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(PARI) IsInList(v, k) = for(i=1, #v, if(v[i]==k, return(1))); return(0) IsInDiff(v, k) = for(i=2, #v, if(abs(v[i]-v[i-1])==k, return(1))); return(0) NextA140778(v)={ local(i, d); if(#v==0, return(1)); i=2; while(1, d=abs(i-v[ #v]); if(!(i==d || IsInList(v, i) || IsInDiff(v, i) || IsInList(v, d) || IsInDiff(v, d)), return(i)); i++) } v=[]; for(i=1, 100, v=concat(v, NextA140778(v))); v
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CROSSREFS
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Cf. A140779, A081145.
See also A005228, A030124, A037257, A037258, A037259, A061577.
Adjacent sequences: A140775 A140776 A140777 this_sequence A140779 A140780 A140781
Sequence in context: A141205 A084582 A072098 this_sequence A095115 A141214 A027379
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KEYWORD
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easy,nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 29 2008
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