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
Examples
244 of the sequence forms a pair with 2196 and we indeed have T(244)+T(2196)=29890+2412306=2442196.
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
Programs
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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 *)
Extensions
Two more terms from Robert G. Wilson v, Jun 21 2004
Terms from a(19) onwards from David Wasserman, May 14 2007
Comments