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A050759
Numbers k such that the decimal expansion of (k^2 + k)/2 (the k-th triangular number) contains no pair of consecutive equal digits.
2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 68, 69, 70, 72, 73, 75, 76, 78, 79, 80, 82, 83, 84, 86, 87, 88
OFFSET
1,3
LINKS
MAPLE
filter:= proc(n) local t;
t:= convert(n*(n+1)/2, base, 10);
not member(0, t[2..-1]-t[1..-2])
end proc:
select(filter, [$0..100]); # Robert Israel, Oct 14 2024
MATHEMATICA
Select[Range[0, 88], FreeQ[Differences[IntegerDigits[(#^2+#)/2]], 0]&] (* Jayanta Basu, May 31 2013 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, Sep 15 1999
EXTENSIONS
Name clarified and offset changed to 1 by Jon E. Schoenfield, Oct 16 2019
STATUS
approved