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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
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
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.)