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A195744
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a(n) = 15*2^(n+1) + 1.
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12
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31, 61, 121, 241, 481, 961, 1921, 3841, 7681, 15361, 30721, 61441, 122881, 245761, 491521, 983041, 1966081, 3932161, 7864321, 15728641, 31457281, 62914561, 125829121, 251658241, 503316481, 1006632961, 2013265921, 4026531841, 8053063681, 16106127361
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OFFSET
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0,1
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COMMENTS
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Binary numbers of form 1111(0^n)1 where n is the index and number of 0's.
Base 10 numbers of this sequence always end in 1.
An Engel expansion of 1/15 to the base 2 as defined in A181565, with the associated series expansion 1/15 = 2/31 + 2^2/(31*61) + 2^3/(31*61*121) + 2^4/(31*61*121*241) + ... . - Peter Bala, Oct 29 2013
The only squares in this sequence are 121 = 11^2 and 961 = 31^2. - Antti Karttunen, Sep 24 2023
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LINKS
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FORMULA
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G.f.: (31-32*x)/(1-3*x+2*x^2).
a(n) = 2*a(n-1)-1.
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EXAMPLE
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First few terms in binary are 11111, 111101, 1111001, 11110001, 111100001.
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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