A230863 a(1)=0; thereafter a(n) = 2^(a(ceiling(n/2)) + a(floor(n/2))).
0, 1, 2, 4, 8, 16, 64, 256, 4096, 65536, 16777216, 4294967296, 1208925819614629174706176, 340282366920938463463374607431768211456, 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576
Offset: 1
Keywords
Links
- Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.
Programs
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Maple
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)];
Formula
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)).
Comments