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Lazy caterer's numbers (A000124) that are also cake numbers (A000125).
0

%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