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A072201
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a(n) = 4*a(n-1) + 1, a(1) = 15.
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3
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15, 61, 245, 981, 3925, 15701, 62805, 251221, 1004885, 4019541, 16078165, 64312661, 257250645, 1029002581, 4116010325, 16464041301, 65856165205, 263424660821, 1053698643285, 4214794573141, 16859178292565
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OFFSET
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1,1
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COMMENTS
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These are the integers N which on application of the Collatz function yield the number 23. The Collatz function: if N is an odd number then (3N+1)/2^r yields a positive odd integer for some value of r (which in this case is 11).
Numbers whose binary representation is 1111 together with n - 1 times 01. For example, a(4) = 981 = 1111010101 (2). - Omar E. Pol, Nov 24 2012
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LINKS
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FORMULA
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a(n) = (23*4^n - 2)/6.
a(n) = 5*a(n-1) - 4*a(n-2).
G.f.: x*(15-14*x)/((1-x)*(1-4*x)). (End)
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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N. Rathankar (rathankar(AT)yahoo.com), Jul 03 2002
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EXTENSIONS
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STATUS
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approved
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