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A230863
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a(1)=0; thereafter a(n) = 2^(a(ceiling(n/2)) + a(floor(n/2))).
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2
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0, 1, 2, 4, 8, 16, 64, 256, 4096, 65536, 16777216, 4294967296, 1208925819614629174706176, 340282366920938463463374607431768211456, 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576
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OFFSET
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1,3
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COMMENTS
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a(16) = 2^512
= 134078079299425970995740249982058461274793658205923933777235\
614437217640300735469768018742981669034276900318581864860508537538828119465\
69946433649006084096.
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LINKS
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Table of n, a(n) for n=1..15.
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory, 2022 (to appear).
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FORMULA
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In general, for n >= 11, define i by 9*2^(i-1) < n <= 9*2^i. Then it appears that a(n) = 2^2^2^...^2^x, a tower of height i+5, containing i+4 2's, where x is in the range 0 < x <= 1.
For example, if n=18, i=1, and a(18) = 2^8192 = 2^2^2^2^2^0.91662699..., of height 6.
Note also that i+5 = A230864(a(n)).
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MAPLE
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f:=proc(n) option remember;
if n=1 then 0 else 2^(f(ceil(n/2))+f(floor(n/2))); fi; end;
[seq(f(n), n=1..16)];
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CROSSREFS
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Cf. A230864, A230874, A230875.
Sequence in context: A076086 A246907 A074700 * A322037 A013133 A012997
Adjacent sequences: A230860 A230861 A230862 * A230864 A230865 A230866
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Nov 02 2013; revised Mar 26 2014
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STATUS
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approved
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