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Search: id:A084760
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| A084760 |
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Squarefree numbers in ascending order such that difference of successive terms is unique. a(m)-a(m-1) = a(k)-a(k-1) iff m = k. |
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+0
1
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| 2, 3, 5, 10, 13, 17, 23, 30, 38, 47, 57, 69, 82, 93, 107, 122, 138, 155, 173, 193, 214, 233, 255, 278, 302, 327, 353, 381, 410, 437, 467, 498, 530, 563, 597, 633, 670, 705, 743, 782, 822, 863, 905, 949, 994, 1037, 1085, 1131, 1178, 1227, 1277, 1329, 1382, 1433
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The sequence of successive difference is 1,2,5,3,4,6,7,8,9,10,12,13,11,14,15,16,17,18,20,21,19,... Conjecture:(1) every number is a term of this sequence. For every number r there exists some k such that a(k) - a(k-1)= r. Question: What is the longest string of consecutive integers in this sequence ( of successive differences)?
Answer: 5, as exemplified by the 6 values 17 to 57. Any longer series with differences consecutive integers must include a multiple of 4, as can be seen by enumerating all possibilities modulo 4. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 14 2006
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EXAMPLE
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After 5 the next term is 10 and not 6 or 7, as 6-5 = 3-2 =1 and 7-5 = 5-3 = 2.
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CROSSREFS
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Cf. A084758, A084759.
Sequence in context: A129281 A022426 A005677 this_sequence A103746 A071848 A120938
Adjacent sequences: A084757 A084758 A084759 this_sequence A084761 A084762 A084763
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 17 2003
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 14 2006
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