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A096032 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 b. 6
1, 415, 1545, 1726, 2196, 910, 3676, 3846, 910, 5226, 415, 6970, 7171, 8526, 9231, 9300, 9756, 9850, 9880, 44835, 9880, 9850, 9756, 9300, 9231, 52830, 8526, 7171, 6970, 5226, 3846, 3676, 2196, 1726, 1545, 84906, 89386, 99580, 99580, 89386, 84906 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For values of a see A096031.
It is easier to generate the pairs sorted by b. A d-digit number b is a member iff 4*(10^(2*d)-10^d-b^2+b)+1 is a square. All such b occur twice, except for 1, which occurs once. There are no members with 2, 6, 7, or 8 digits. There are six distinct nine-digit members. - David Wasserman, May 15 2007
REFERENCES
J. S. Madachy, Madachy's Mathematical Recreations, pp. 166 Dover NY 1979.
LINKS
EXAMPLE
1726 of the sequence forms a pair with 150 and we indeed have T(150)+T(1726)=11325+1490401=1501726.
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: A187864 A190028 A184545 * A166057 A306381 A172779
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 15 2007
STATUS
approved

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Last modified May 21 13:13 EDT 2024. Contains 372736 sequences. (Running on oeis4.)