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A213518
Numbers n such that the triangular number n*(n+1)/2 has 2 different digits in base 10.
3
4, 5, 6, 7, 8, 9, 12, 13, 18, 24, 34, 44, 58, 66, 77, 100, 101, 105, 109, 114, 132, 141, 363, 666, 714, 816, 1000, 1095, 1287, 1332, 1541, 3363, 6666, 10000, 10114, 13332, 66666, 100000, 133332, 666666, 1000000, 1333332, 6666666, 10000000, 13333332, 33336636, 66666666, 100000000
OFFSET
1,1
COMMENTS
The list of triangular numbers containing only one digit (A045914) is finite. This list is infinite because numbers like 133332, 666666, and 1000000 occur an infinite number of times.
A118668(a(n)) = 2. - Reinhard Zumkeller, Jul 11 2015
For n > 2, A325907(n) is a term. - Seiichi Manyama, Sep 15 2019
LINKS
Seiichi Manyama and T. D. Noe Table of n, a(n) for n = 1..60 (first 51 terms from Seiichi Manyama)
MATHEMATICA
t = {}; Do[tri = n*(n+1)/2; If[Length[Union[IntegerDigits[tri]]] == 2, AppendTo[t, n]], {n, 10^5}]; t
PROG
(Haskell)
a213518 n = a213518_list !! (n-1)
a213518_list = filter ((== 2) . a118668) [0..]
-- Reinhard Zumkeller, Jul 11 2015
(PARI) for(k=0, 1e8, if(#Set(digits(k*(k+1)/2))==2, print1(k", "))) \\ Seiichi Manyama, Sep 15 2019
CROSSREFS
Cf. A062691 (the corresponding triangular numbers), A213516, A213517, A325907.
Cf. A118668.
Cf. A187127.
Sequence in context: A321353 A161674 A285623 * A214419 A189481 A123977
KEYWORD
nonn,base
AUTHOR
T. D. Noe, Jun 22 2012
EXTENSIONS
a(45)-a(48) from Seiichi Manyama, Sep 15 2019
STATUS
approved