cp's OEIS Frontend

A117462 The number of doubling steps of SOD(n) to exceed or equal n.

%I A117462 #24 Aug 20 2024 18:39:29
%S A117462 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,
%T A117462 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,
%U A117462 3,4,4,3,3,3,3,3,3,3,3,4,4,4,3,3,3,3,3,3,3,4
%N A117462 The number of doubling steps of SOD(n) to exceed or equal n.
%C A117462 "SOD" = "sum of digits".
%F A117462 Take n, calculate SOD, and count doubling iterations (at least 1) to equal or exceed n.
%F A117462 a(n) = max(1, log_2(n/A007953(n))). - _R. J. Mathar_, Sep 24 2018
%e A117462 a(10) = 4. SOD(10)=1. 1 doubled is 2. Iterating: 2,4,8,16 -- 4 iterations of doubling 1 to exceed 10.
%p A117462 A117462 := proc(n)
%p A117462     local x;
%p A117462     x := digsum(n) ;
%p A117462     max(1,ceil(log[2](n/x))) ;
%p A117462 end proc:
%p A117462 seq(A117462(n),n=1..90) ; # _R. J. Mathar_, Sep 24 2018
%t A117462 Array[Max[1, Ceiling@ Log2[#/Total@ IntegerDigits@ #]] &, 105] (* _Michael De Vlieger_, Sep 24 2018 *)
%o A117462 (BASIC)
%o A117462 10 'use of str,mid,len,val
%o A117462 20 'number of doubled iterations required to equal or exceed sod(n)
%o A117462 30 C=C+1
%o A117462 40 D=str(C)
%o A117462 50 E=len(D)
%o A117462 60 for Q=2 to E
%o A117462 70 A=mid(D,Q,1):G=val(A)
%o A117462 80 I=I+G
%o A117462 90 next Q
%o A117462 100 print C;I;"-";
%o A117462 110 K=I
%o A117462 120 I=0
%o A117462 130 for R=1 to C
%o A117462 140 K=K+K:T=T+1
%o A117462 150 if K>=C then print C;K;T:cancel for:stop:goto 170
%o A117462 160 next R
%o A117462 170 K=0:T=0
%o A117462 180 goto 30
%Y A117462 Cf. A007953, A117463.
%K A117462 easy,nonn,base
%O A117462 1,10
%A A117462 _Enoch Haga_, Mar 18 2006
%E A117462 Re-engineered definition from BASIC program, and corrected/clarified the terms. - _R. J. Mathar_, Sep 24 2018