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Search: id:A130335
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| A130335 |
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Smallest k>0 such that GCD(n*(n+1)/2,(n+k)*(n+k+1)/2)=1. |
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+0
5
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| 1, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 13, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 7, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 13, 2, 2, 10, 2, 2, 4, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2, 2, 4, 2, 2, 4, 2, 2, 22, 2, 2, 7, 2, 2, 16, 2, 2, 4, 2, 2, 10, 2, 2, 7, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = Min{k>0: A050873(A000217(n+k),A000217(n))=1);
a(n) = A130334(n) - n;
a(n) > 1 for n>1; a(n) > 2 iff n mod 3 = 0: a(A001651(n))=2, a(A008585(n))>2 for n>1.
First occurrence of 3k+1, k=0.. or 0 if unknown, limit = 2^31: 1, 6, 3, 12, 24, 90, 231, 84, 792, 0, 195, 3432, 780, 0, 3255, 6075, 73644, 51482970, 0, 924, 183540, 0, 45219, 0, 509124, 3842375445, 29259, 71484, 0, 0, 0, 2311539, 238547880, 0, 55380135, 893907420, 23303784, 0, 0, 208260975, 0, 0, 1744264599, 0, 0, 0, 1487657079, 665710275, 0, 0, 1963994955, 0, 319589424, 0, 0, 0, 4181294964, 0, 0, 383229924, ..., . - Robert G. Wilson v (rgwv(at)rgwv.com), Jun 03 2007.
a(n) (mod 3) == 1 if a(n) # 2. - Robert G. Wilson v (rgwv(at)rgwv.com), Jun 03 2007.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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f[n_] := Block[{k = If[ n == 1 || Mod[n, 3] == 0, 1, 2]}, While[ GCD[n(n + 1)/2, (n + k)(n + k + 1)/2] != 1, k += 3 ]; k]; Array[f, 100] (* from Robert G. Wilson v (rgwv(at)rgwv.com), Jun 03 2007 *)
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CROSSREFS
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See A130336 and A130337 for record values and where they occur.
Adjacent sequences: A130332 A130333 A130334 this_sequence A130336 A130337 A130338
Sequence in context: A023399 A082072 A082066 this_sequence A073246 A021790 A011048
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 28 2007
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