A096031 Take pairs (a, b), sorted on a, such that T(a)+T(b)=concatenation of a and b, where T(k) is the k-th triangular number A000217(k). Sequence gives values of a.

19, 90, 120, 150, 244, 585, 700, 769, 1414, 1474, 1909, 2829, 3030, 4774, 6154, 6324, 7804, 8274, 8455, 10614, 11544, 11725, 12195, 13675, 13845, 15094, 15225, 16969, 17170, 18525, 19230, 19299, 19755, 19849, 19879, 47170, 55165, 90844, 109155

Offset

1,1

Comments

For values of b see A096032.

References

J. S. Madachy, Madachy's Mathematical Recreations, pp. 166 Dover NY 1979.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..294

Example

244 of the sequence forms a pair with 2196 and we indeed have T(244)+T(2196)=29890+2412306=2442196.

Mathematica

f[n_] := Block[{k = n + 1, t1 = n(n + 1)/2, td = IntegerDigits[n]}, While[k < 15*n && t1 + k(k + 1)/2 != FromDigits[ Join[ td, IntegerDigits[k]]], k++ ]; If[k != 15*n, k, 0]]; Do[ k = f[n]; If[k != 0, Print[n, " & ", k]], {n, 10^6}] (* Robert G. Wilson v, Jun 21 2004 *)

Crossrefs

Sequence in context: A347364 A224097 A088574 * A302710 A157875 A039409

Adjacent sequences: A096028 A096029 A096030 * A096032 A096033 A096034

Keyword

nonn,base

Author

Lekraj Beedassy, Jun 16 2004

Extensions

Two more terms from Robert G. Wilson v, Jun 21 2004

Terms from a(19) onwards from David Wasserman, May 14 2007

Status

approved