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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 24 00:02 EDT 2024. Contains 373661 sequences. (Running on oeis4.)