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 A230303 Let M(1)=0 and for n >= 2, let B(n)=M(ceiling(n/2))+M(floor(n/2))+2, M(n)=2^B(n)+M(floor(n/2))+1; sequence gives M(n). 12
 0, 5, 129, 4102, 87112285931760246646623899502532662132742, 1852673427797059126777135760139006525652319754650249024631321344126610074239106 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS M(n) is the smallest value of k such that A228085(k) = n. For example, 129 is the first time a 3 appears in A228085 (and is therefore the first term in A230092). M(4) = 4102 is the first time a 4 appears in A228085 (and is therefore the first term in A227915). REFERENCES Max A. Alekseyev, Donovan Johnson and N. J. A. Sloane, On Kaprekar's Junction Numbers, in preparation, 2017. LINKS FORMULA Define i by 2^(i-1) < n <= 2^i. Then it appears that a(n) = 2^2^2^...^2^x a tower of height i+3, containing i+2 2's, where x is in the range 0 < x <= 1. For example, if n=7, i=3, and a(18) = 2^4233+130 = 2^2^2^2^2^.88303276... Note also that i+2 = A230864(a(n)). EXAMPLE The terms are 0, 2^2+0+1, 2^7+0+1, 2^12+5+1, 2^136+5+1, 2^160+129+1, 2^4233+129+1, 2^8206+4102+1, 2^k+4102+1 with k=2^136+4110, ... . The length (in bits) of the n-th term is A230302(n)+1. MAPLE f:=proc(n) option remember; local B, M; if n<=1 then RETURN([0, 0]); else if (n mod 2) = 0 then B:=2*f(n/2)+2; else B:=f((n+1)/2)+f((n-1)/2)+2; fi; M:=2^B+f(floor(n/2))+1; RETURN([B, M]); fi; end proc; [seq(f(n), n=1..6)]; CROSSREFS Cf. A228085, A230092, A227915, A230093, A230302 (for B(n)), A230864. Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064. Sequence in context: A316986 A316392 A277259 * A094074 A012218 A012136 Adjacent sequences:  A230300 A230301 A230302 * A230304 A230305 A230306 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 24 2013; Mar 26 2014 STATUS approved

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Last modified January 20 14:02 EST 2020. Contains 331094 sequences. (Running on oeis4.)