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A227218
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Smallest triangular number ending in n ones.
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3
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1, 1711, 105111, 6271111, 664611111, 222222111111, 22222221111111, 2222222211111111, 2517912111111111, 18428299161111111111, 2222222222211111111111, 222222222222111111111111, 22222222222221111111111111, 1090161504430911111111111111
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OFFSET
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1,2
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COMMENTS
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If a triangular number ends in like digits then it can only end in 0's, 1's, 5's or 6's.
The sequence is infinite because the sequence of triangular numbers 21, 2211, 222111, 22221111, ... (A319170) is infinite.
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LINKS
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EXAMPLE
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a(2) = 1711 because 1711 is the smallest triangular number ending in 2 '1's.
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MATHEMATICA
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t = {}; Do[Do[x = n*(n + 1)/2; If[Mod[x, 10^m] == (10^m - 1)/9, AppendTo[t, x]; Break[]], {n, 1, 10^m}], {m, 1, 10}]; t
a[n_] := Block[{x, y, s}, s = y /. List@ ToRules[ Reduce[(y+1)* y/2 == x*10^n +(10^n - 1)/9 && y > 0 && x >= 0, {y, x}, Integers] /. C[1] -> 0]; Min[s*(s + 1)/2]]; Array[a, 20] (* Giovanni Resta, Sep 20 2013 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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