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A054236
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Consider all integer triples (i,j,k), j,k>0, with i^3=j^3+binomial(k+2,3), ordered by increasing i; sequence gives k values.
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3
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6, 19, 132, 182, 217, 757, 2377, 2077, 2833, 4374, 2408, 4864, 4912, 6097, 7295, 3324, 8341, 13357, 17522, 20006, 25939, 20406, 24492, 68984, 75732, 69151, 79000, 69361, 97598, 99064, 126014, 126873, 154622, 174278, 180514, 136431, 117151, 198310
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