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Search: id:A068776
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| A068776 |
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a(0) = 1; for n > 0, a(n) is the smallest triangular number which is a (proper) multiple of a(n-1). |
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+0
4
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| 1, 3, 6, 36, 2016, 1493856, 579616128, 11013286048128, 1004811205553955491328, 1897191992473259952000123882626029056, 5012064437680248664058937311304485563631765718940918773832320000
(list; graph; listen)
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OFFSET
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0,2
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EXAMPLE
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a(2) = 6, since 6 = 2*a(1) and 6 is a triangular number.
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MATHEMATICA
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pm1[{k_}] := {1, k-1}; pm1[lst_] := Module[{a, m, v}, a=lst[[1]]; m=Times@@Rest[lst]; v=pm1[Rest[lst]]; Union[ChineseRemainder[{1, #}, {a, m}]&/@v, ChineseRemainder[{-1, #}, {a, m}]&/@v]]; nexttri[1]=3; nexttri[n_] := Module[{s}, s=(pm1[Power@@#&/@FactorInteger[4n]]^2-1)/8; For[i=1, True, i++, If[s[[i]]>n, Return[s[[i]]]]]]; a[0]=1; a[n_] := a[n]=nexttri[a[n-1]]; (* First do <<NumberTheory`NumberTheoryFunctions`. If lst is a list of relatively prime integers >= 3, pm1[lst] is the list of numbers less than their product and == 1 or -1 (mod every element of lst). nexttri[n] is the smallest triangular number >n and divisible by n. *)
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PROGRAM
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(PARI) {a068776(m)=local(k, q, n); k=1; q=k*(k+1)/2; while(q<m, n=q; print1(n, ", "); k++; q=q+k; while(q<m&&q%n>0, k++; q=q+k))}
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CROSSREFS
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Cf. A000217, A068142.
Sequence in context: A048642 A077532 A093800 this_sequence A025596 A114038 A000222
Adjacent sequences: A068773 A068774 A068775 this_sequence A068777 A068778 A068779
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 01 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Mar 09 2002
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