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

1,10

Comments

"SOD" = "sum of digits".

Links

Table of n, a(n) for n=1..90.

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

Example

a(10) = 4. SOD(10)=1. 1 doubled is 2. Iterating: 2,4,8,16 -- 4 iterations of doubling 1 to exceed 10.

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

Mathematica

Array[Max[1, Ceiling@ Log2[#/Total@ IntegerDigits@ #]] &, 105] (* Michael De Vlieger, Sep 24 2018 *)

Prog

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

Crossrefs

Cf. A007953, A117463.

Sequence in context: A237524 A266143 A171623 * A155462 A109496 A138851

Adjacent sequences: A117459 A117460 A117461 * A117463 A117464 A117465

Keyword

easy,nonn,base

Author

Enoch Haga, Mar 18 2006

Extensions

Re-engineered definition from BASIC program, and corrected/clarified the terms. - R. J. Mathar, Sep 24 2018

Status

approved