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A260117 Smallest triangular number that is pandigital in base n.

%I A260117 #16 Sep 29 2017 23:23:50
%S A260117 6,15,78,990,8385,128271,2293011,46923828,1062489753,27403863105,
%T A260117 757016521030,24028339652778,807863408487460,29499468896141965,
%U A260117 1162871296355724735,49093065731151773880,2200689210818047715703,104755000778178115071015,5271254575974180914006953
%N A260117 Smallest triangular number that is pandigital in base n.
%C A260117 Presumably, lim_{n->infinity} a(n)/A049363(n) = 1.
%H A260117 Chai Wah Wu, <a href="/A260117/b260117.txt">Table of n, a(n) for n = 2..28</a> (n = 2..22 from Jon E. Schoenfield)
%e A260117 Using the letters a, b, c, ... to represent digit values 10, 11, 12, ..., the terms are as follows:
%e A260117 .
%e A260117    n            a(n) in base 10  a(n) in base n
%e A260117   ==  =========================  ==============
%e A260117    2                          6  110_2
%e A260117    3                         15  120_3
%e A260117    4                         78  1032_4
%e A260117    5                        990  12430_5
%e A260117    6                       8385  102453_6
%e A260117    7                     128271  1042653_7
%e A260117    8                    2293011  10576423_8
%e A260117    9                   46923828  107258346_9
%e A260117   10                 1062489753  1062489753_10
%e A260117   11                27403863105  10692847a53_11
%e A260117   12               757016521030  10286b37459a_12
%e A260117   13             24028339652778  1053b2a49c786_13
%e A260117   14            807863408487460  1036cb2487d59a_14
%e A260117   15          29499468896141965  102568d3be749ca_15
%e A260117   16        1162871296355724735  102359486ac7edbf_16
%e A260117   17       49093065731151773880  1029a46d78g53cbef_17
%e A260117   18     2200689210818047715703  10237c486geh5bdaf9_18
%e A260117   19   104755000778178115071015  10236a47589cgdfeibh_19
%e A260117   20  5271254575974180914006953  10235i96e4jb8gfcah7d_20
%o A260117 (PARI) A049363(n)=if(n>1, (n^n-n)/(n-1)^2+n^(n-2)*(n-1)-1, 1)
%o A260117 a(n)=my(k=ceil((sqrt(8*A049363(n)+1)-1)/2),t); while(#Set(digits(t=binomial(k+1,2),n))<n, k++); t \\ _Charles R Greathouse IV_, Jul 17 2015
%Y A260117 Cf. A049363.
%K A260117 nonn,base
%O A260117 2,1
%A A260117 _Jon E. Schoenfield_, Jul 17 2015