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A081847
a(1) = 1, a(n) = smallest positive number such that the concatenation of a(n-1) and a(n) is a triangular number not obtained earlier.
2
1, 5, 5, 28, 50, 50, 403, 651, 511, 566, 16, 53, 56, 1, 20, 16, 110, 26, 28, 203, 203, 841, 753, 378, 885, 115, 440, 391, 6, 6, 30, 81, 28, 441, 330, 891, 1, 36, 55, 65, 55, 278, 631, 90, 3, 6, 66, 70, 3, 25, 3, 51, 51, 360, 46, 5, 95, 91, 80, 200, 661, 825, 6, 105, 85
OFFSET
1,2
COMMENTS
From Robert Israel, Dec 30 2018: (Start)
All terms end in 0, 1, 3, 5, 6 or 8.
Triangular numbers that cannot be obtained as concatenation of a(n-1) and a(n) include 1, 3, 6, 10, 21, 28, 45, 78, 91. (End)
LINKS
EXAMPLE
a(2) = 5 and a(3) = 28 and 528 is a triangular number.
MAPLE
Seen:= {}:
A[1]:= 1:
maxb:= 1:
for n from 2 to 100 do
found:= false;
for d from 1 while not found do
r:= A[n-1]*10^d;
x0:= r + 10^(d-1);
for m from ceil((sqrt(1+8*x0)-1)/2) do
x:= m*(m+1)/2;
if x >= r + 10^d then break fi;
if not member(x, Seen) then
A[n]:= x - r;
Seen:= Seen union {x};
found:= true;
break
fi
od od od:
seq(A[n], n=1..100); # Robert Israel, Dec 31 2018
CROSSREFS
Sequence in context: A302000 A219351 A130220 * A203124 A305180 A284140
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Apr 10 2003
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003
Edited by Robert Israel, Dec 30 2018
STATUS
approved