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%I #11 Jan 22 2020 14:47:00
%S 1,2,4,232,15226
%N Lazy caterer's numbers (A000124) that are also cake numbers (A000125).
%C a(6) > 10^36, if it exists. - _Bert Dobbelaere_, Jan 18 2020
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cake_number">Cake number</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence">Lazy caterer's sequence</a>.
%e The indices i and j such that a(n) = A000124(i) = A000125(j):
%e n a(n) i j
%e 1 1 0 0
%e 2 2 1 1
%e 3 4 2 2
%e 4 232 21 11
%e 5 15226 174 45
%t lazyCatererQ[n_] := IntegerQ @ Sqrt[8*n - 7]; cake[n_] := Binomial[n, 3] + n; Select[Table[cake[n], {n, 0, 100}], lazyCatererQ]
%Y Cf. A000124, A000125.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Nov 29 2019