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Search: id:A118711
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| A118711 |
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Integers n such that the n-th triangular number t_n has all its base 12 digits contained in {1,5,7,11}. |
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1
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| 1, 13, 61, 82, 898, 2962, 2989, 9133, 20077, 20653, 28669, 29266, 35581, 35842, 37501, 99133, 236674, 286717, 424621, 424957, 821698, 941650, 1704301, 1722370, 2978413, 3328258, 4494466, 10022317, 40392829, 49870141, 50668882, 53933053
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In base 12 all primes greater than 3 end in the digits 1, 5, 7, E, where X is 10 and E is 11. They are the digits that satisfies GCD(d,12)=1.
The sequence in base 12 is: 1, 11, 51, 6X, 62X, 186X, 1891, 5351, E751, EE51, 14711, 14E2X, 18711, 188XX, 19851, 49451, E4E6X, 119E11, 185891, 185E11, 33762X, 394E2X, 6X2351, 6E08XX, EE7751, 11460XX, 1608E6X, 3433E51, 1163E591, 14850051, 14E7632X, 1608E311, 18331451, 1870E191, 1974E311, ..., . Note that all elements end in 1 or X. The corresponding triangular numbers after the first end in the digits 17 or 77, but not respectively.
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FORMULA
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a(n)=m if the m-th triangular number t_m=m*(m+1)/2 has its base 12 digits contained in {1,5,7,11}.
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EXAMPLE
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a(4)=82=6X since the triangular number t=82*(82+1)/2=3403=1E77.
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MAPLE
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L:=[]: pd:={1, 5, 7, 11}: for w to 1 do for n from 1 to 10^6 do t:=n*(n+1)/2; lod:=convert(t, base, 12); sod:=convert(lod, set); if sod subset pd then L:=[op(L), [n, t]] fi; od od; L;
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MATHEMATICA
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fQ[n_] := Union@ Join[{1, 5, 7, 11}, IntegerDigits[n(n + 1)/2, 12]] == {1, 5, 7, 11}; Do[ If[fQ@n, AppendTo[lst, n]], {n, 10^8}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000217, A119033, A119034.
Sequence in context: A146764 A145474 A002647 this_sequence A028874 A087106 A142402
Adjacent sequences: A118708 A118709 A118710 this_sequence A118712 A118713 A118714
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KEYWORD
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nonn,base
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AUTHOR
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Walter Kehowski (wkehowski(AT)cox.net), May 24 2006
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EXTENSIONS
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Edited and extended a(23)-a(32) by Robert G. Wilson v (rgwv(at)rgwv.com), Jun 20 2006
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