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A118706
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Triangular numbers whose digits in base 12 are contained in {1,5,7,11}.
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0
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1, 91, 1891, 3403, 403651, 4388203, 4468555, 41710411, 201553003, 213283531, 410970115, 428264011, 633021571, 642342403, 703181251, 4913725411, 28007409475, 41103462403, 90151709131, 90294438403, 337594212451
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OFFSET
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1,2
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COMMENTS
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In base 12 all primes greater than 3 end in a 1, 5, 7, or E, where X is 10 and E is eleven. In base 12 the sequence is 1, 77, 1117, 1E77, 175717, 1577577, 15E5E77, 11E75E77, 575EE577, 5E517E77, E5771E17, EE511E77, 157EE7E17, 15E151E17, 1775E1717, E5171E117, 551775E717, 7E71571E17, 1557E75EE77, 155EE511E17, 55517751117, 71E11E71E77. Note that all elements after the first either end in 17 or 77. In base 12 the n such that t=n(n+1)/2 end in the digits 1 or X, but not respectively.
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LINKS
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Table of n, a(n) for n=1..21.
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FORMULA
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a(n)=t if t is the n-th triangular number such that S subset {1,5,7,11}, where S is the set of digits of t in base 12.
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EXAMPLE
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a(4)=3403=1E77 in base 12.
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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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Select[Accumulate[Range[822000]], SubsetQ[{1, 5, 7, 11}, IntegerDigits[ #, 12]]&] (* Harvey P. Dale, Oct 18 2019 *)
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CROSSREFS
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Cf. A000217, A119033, etc.
Sequence in context: A254611 A184462 A229518 * A119150 A008394 A332949
Adjacent sequences: A118703 A118704 A118705 * A118707 A118708 A118709
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KEYWORD
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nonn,base
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AUTHOR
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Walter Kehowski, May 24 2006
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STATUS
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approved
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