Question 861717: 6-9-?-24-36
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! a(n) = (3/2)a(n-1) if a(n-1) is even;
a(n) = (3/2)(a(n-1)+1) if a(n-1) is odd.
6,9,_,24,36
6, 9, 15, 24, 36, 54, 81, 123, 186, 279, 420, 630, 945, 1419, 2130, 3195, 4794, 7191, 10788, 16182, 24273, 36411, 54618, 81927, 122892, 184338, 276507, 414762, 622143, 933216, 1399824, 2099736, 3149604, 4724406, 7086609, 10629915
There are many other possibilities too.
Numbers n such that 1 and 2 occur juxtaposed in the base 4 representation of n but not of n-1.
6, 9, 22, 24, 36, 41, 54, 57, 70, 73, 86, 88, 96, 118, 121, 134, 137, 144, 164, 169, 182, 185, 198, 201, 214, 216, 228, 233, 246, 249, 262, 265, 278, 280, 292, 297, 310, 313, 326, 329, 342, 344, 352, 374, 377, 384, 454, 457, 470
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