http://www.mapleprimes.com/posts/43769-Ponder-This en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Sun, 14 Jun 2026 02:32:55 GMT Sun, 14 Jun 2026 02:32:55 GMT The latest comments added to the Post, Ponder This http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/43769-Ponder-This http://www.mapleprimes.com/posts/43769-Ponder-This?ref=Feed:MaplePrimes:Ponder This:Comments#comment80772 Nice improvement, Alec, thanks. Slightly clearer, I think, and a bit faster is to replace trunc( (...)/i) with iquo( (...), i). Faster yet (still not by much) is to replace the three calls to irem() with a single call that assigns a local variable. One implementation is <pre> Sols3 := proc(b) local A,i,j,k,arem,rem; arem := proc() rem := irem(b*j,i) end; A := table(); A[1] := [$1..b-1]; for i from 2 do A[i] := [seq](seq(b*j+k*i-rem ,k = `if`(arem()=0,0,1) .. iquo(b-1+rem,i)) ,j = A[i-1]); if A[i] = [] then break fi od; i-1 = A[i-1] end proc: </pre> The latest comments added to the Post, Ponder This 80772 Sat, 06 Aug 2005 19:32:18 Z Joe Riel Joe Riel http://www.mapleprimes.com/posts/43769-Ponder-This?ref=Feed:MaplePrimes:Ponder This:Comments#comment80769 Meanwhile, I calculated a(16): 39 = [18872900738885736149574055538327802527212537551, 60753927368683934227793588395570842550542338031, 89515749136034833729775437005460258167590093634] Converted to hex, the numbers look like 34E4A468166CD8604EC0F8106AB4326098286CF AA44CE207C78FC30003C3CC0D8382E2078D07EF FAE06678C2E884607EB8B4E0B0A0F0603420342 The latest comments added to the Post, Ponder This 80769 Sun, 07 Aug 2005 00:06:18 Z alec alec http://www.mapleprimes.com/posts/43769-Ponder-This?ref=Feed:MaplePrimes:Ponder This:Comments#comment86928 Thank you, Joe. Both things are good. The next improvement can be achieved by separating the loop in 2 parts, <pre>a:=proc(b) local A,i,j,k,arem,brem,rem; arem:=proc() rem:= irem(b*j,i); seq(b*j+k*i-rem,k = `if`(rem=0,0,1) .. iquo(b-1+rem,i)) end; brem:=proc() rem:=irem(b*j,i); if rem=0 then b*j elif b-1+rem&lt;i then NULL else b*j+i-rem fi end; A[1] := [$1..b-1]; for i from 2 to b-1 do A[i] := [seq](arem(), j = A[i-1]) od; for i from b do A[i] := [seq](brem(), j = A[i-1]); if A[i] = [] then break fi od; i-1 = A[i-1] end:</pre> The latest comments added to the Post, Ponder This 86928 Sun, 07 Aug 2005 12:34:34 Z alec alec http://www.mapleprimes.com/posts/43769-Ponder-This?ref=Feed:MaplePrimes:Ponder This:Comments#comment80767 Looking at my user number, 135, Joe Riel's 84, and Thomas Richard's 50, I found out that we have something in common. <code> gcd(50,84)=2 gcd(50,135)=5 gcd(84,135)=3 </code> The latest comments added to the Post, Ponder This 80767 Mon, 08 Aug 2005 03:32:04 Z alec alec http://www.mapleprimes.com/posts/43769-Ponder-This?ref=Feed:MaplePrimes:Ponder This:Comments#comment90124 Correspondingly, here is the improved version of a1, <pre>a1:=proc(b) local A,i,j,k,arem,rem,dig; arem:=proc() rem:=irem(b*j,i); dig:=convert(j,base,b); seq(`if`(member(k*i-rem,dig),NULL,b*j+k*i-rem), k = 1 .. iquo(b-1+rem,i)) end; A[1] := [$1..b-1]; for i from 2 do A[i] := [seq](arem(), j = A[i-1]); if A[i] = [] then break fi od; i-1 = A[i-1] end:</pre> For decimal system, it works very fast, <pre>tt:=time(): a1(10); time()-tt; 9 = [381654729] 0.016</pre> In addition to the values in the worksheet, I calculated <pre>a1(21); 18 = [509504810627259318940020] a1(22); 19 = [5213608783930183587520297] a1(23); 21 = [3017921136920002608782486643, 3202513921881602294966195322, 10912277070078955588719411381, 11506928512609494037599575154, 19136629049078922486640055262, 19563154864313291881366262910, 20927442077211608842020972981, 22095893110934309880723905997, 24479055281091281744429147151, 26034588683899462487295851544, 27944901128718982841182304058, 28236074834439966722409861288, 30327538677373615144106864301, 30327538677373615144106864322, 33286709815522787435710859625, 33637644479370238638607793874, 39311846134353288073052119134] </pre> The latest comments added to the Post, Ponder This 90124 Tue, 09 Aug 2005 23:50:49 Z Alec Mihailovs Alec Mihailovs http://www.mapleprimes.com/posts/43769-Ponder-This?ref=Feed:MaplePrimes:Ponder This:Comments#comment90128 Now, compiled procedures should run much faster. Here is the first try, <pre>a2 := proc(b::integer[4], A::Array(datatype = integer[4])):: integer[4]; local i::integer[4], j::integer[4], K::integer[4], s::integer[4], r::integer[4]; A[1] := 1; i := 2; K := 1; s := 1; while 0 &lt; i do if s = 1 then r := irem(A[1], i); for j from 2 to i - 1 do r := irem(r*b + A[j], i) end do; r := irem(r*b, i); if r = 0 then A[i] := 0; K := max(K, i); i := i + 1 elif b - 1 + r &lt; i then i := i - 1; s := 0 else A[i] := i - r; K := max(K, i); i := i + 1 end if else if A[i] + i &lt; b then A[i] := A[i] + i; i := i + 1; s := 1 else i := i - 1 end if end if end do; K end proc: a3:=Compiler:-Compile(a2): A:=Array(1..100,datatype=integer[4]): </pre> While a2 is slower than a, the compiled procedure a3 is much faster. For example, <pre>tt:=time(): a3(10,A); time()-tt; 25 0.016</pre> It should be called as a3(b,A) where b is the base and A is a predefined Array with datatype=integer[4] and length greater than the expected maximal number of digits. It returns the maximal number of digits. In particular, for b from 17 to 21 the maximal number of digits has appeared to be 45, 48, 48, 52, 53. The latest comments added to the Post, Ponder This 90128 Fri, 12 Aug 2005 04:41:53 Z Alec Mihailovs Alec Mihailovs