cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A096031 #14 Jun 15 2020 21:08:34
%S A096031 19,90,120,150,244,585,700,769,1414,1474,1909,2829,3030,4774,6154,
%T A096031 6324,7804,8274,8455,10614,11544,11725,12195,13675,13845,15094,15225,
%U A096031 16969,17170,18525,19230,19299,19755,19849,19879,47170,55165,90844,109155
%N 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.
%C A096031 For values of b see A096032.
%D A096031 J. S. Madachy, Madachy's Mathematical Recreations, pp. 166 Dover NY 1979.
%H A096031 Chai Wah Wu, <a href="/A096031/b096031.txt">Table of n, a(n) for n = 1..294</a>
%e A096031 244 of the sequence forms a pair with 2196 and we indeed have T(244)+T(2196)=29890+2412306=2442196.
%t A096031 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 *)
%K A096031 nonn,base
%O A096031 1,1
%A A096031 _Lekraj Beedassy_, Jun 16 2004
%E A096031 Two more terms from _Robert G. Wilson v_, Jun 21 2004
%E A096031 Terms from a(19) onwards from _David Wasserman_, May 14 2007