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.

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

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

Chai Wah Wu, Table of n, a(n) for n = 1..294

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

Adjacent sequences: A096029 A096030 A096031 * A096033 A096034 A096035

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