|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|