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Search: id:A077214
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| A077214 |
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a(1) = 1. a(n+1) is the smallest number which is greater than a(n), coprime to it and has a different prime signature. |
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+0
1
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| 1, 2, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 37, 38, 41, 42, 43, 44, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Subsidiary sequence: First occurrence of a difference n between successive terms. Conjecture : the maximum value of a(k+1) - a(k) = 7 that too occurs only once for k = 2.( i.e. the subsediary sequence has only 7 terms.)
I conjecture than a(n+1)-a(n) is unbounded. The simplest way to get such a gap is to find n divisible by lcm(1,2,...,k) where n+1 has the same prime signature as n. I expect that such numbers exist, although they are likely to be quite large. (Since n-1 lacks small divisors, it is very likely to be in the sequence and so n is also very likely to be in the sequence.) Note that the sequence includes every prime except 3, 5 and 7. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 18 2006
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CROSSREFS
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Sequence in context: A131463 A065644 A043065 this_sequence A135782 A037457 A037314
Adjacent sequences: A077211 A077212 A077213 this_sequence A077215 A077216 A077217
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 02 2002
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EXTENSIONS
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More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 18 2006
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