A117462 The number of doubling steps of SOD(n) to exceed or equal n.
1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 3, 2, 2, 2, 2, 2, 2, 1, 1, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 4, 4, 3, 3, 3, 3, 3, 3, 2, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4
Offset: 1
Examples
a(10) = 4. SOD(10)=1. 1 doubled is 2. Iterating: 2,4,8,16 -- 4 iterations of doubling 1 to exceed 10.
Programs
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BASIC
10 'use of str,mid,len,val 20 'number of doubled iterations required to equal or exceed sod(n) 30 C=C+1 40 D=str(C) 50 E=len(D) 60 for Q=2 to E 70 A=mid(D,Q,1):G=val(A) 80 I=I+G 90 next Q 100 print C;I;"-"; 110 K=I 120 I=0 130 for R=1 to C 140 K=K+K:T=T+1 150 if K>=C then print C;K;T:cancel for:stop:goto 170 160 next R 170 K=0:T=0 180 goto 30
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Maple
A117462 := proc(n) local x; x := digsum(n) ; max(1,ceil(log[2](n/x))) ; end proc: seq(A117462(n),n=1..90) ; # R. J. Mathar, Sep 24 2018
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Mathematica
Array[Max[1, Ceiling@ Log2[#/Total@ IntegerDigits@ #]] &, 105] (* Michael De Vlieger, Sep 24 2018 *)
Formula
Take n, calculate SOD, and count doubling iterations (at least 1) to equal or exceed n.
a(n) = max(1, log_2(n/A007953(n))). - R. J. Mathar, Sep 24 2018
Extensions
Re-engineered definition from BASIC program, and corrected/clarified the terms. - R. J. Mathar, Sep 24 2018
Comments