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.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A081844 A081845 A081846 * A081848 A081849 A081850

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