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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 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

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