Source Codes for "Gaps Between Integers Having a Common Divisor with an Odd Semi-prime"

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Source Codes for "Gaps Between Integers Having a Common Divisor with an Odd Semi-prime"

Posted: fosuwxb 25 Product: Maple 2021

November 09 2024

Here are the source codes for the paper "Gaps Between Integers Having a Common Divisor with an Odd Semi-prime"

gg := proc (x, y) return abs(x-y)-1 end proc

(1)

CopyArrayElem := proc (x, n) local y, i; y := Array(1 .. n); for i to n do y(i) := x(i) end do; return y end proc

proc (x, n) local y, i; y := Array(1 .. n); for i to n do y(i) := x(i) end do; return y end proc

(2)

$PrintArray := proc (x, n) local i; for i to n do printf("%d, ", x(i)); if i = (1/2)*n then printf("|,") end if end do; printf("\n") end proc$

proc (x, n) local i; for i to n do printf("%d, ", x(i)); if i = (1/2)*n then printf("|,") end if end do; printf("
") end proc

(3)

GapArray := proc (x, n) local i, y; y := Array(1 .. n-1); for i to n-1 do y(i) := gg(x(i), x(i+1)) end do; return y end proc

proc (x, n) local i, y; y := Array(1 .. n-1); for i to n-1 do y(i) := gg(x(i), x(i+1)) end do; return y end proc

(4)

ShiftArrayElem := proc (x, n, d) local i, y; y := Array(1 .. n); for i to n do y(i) := x(i)+d end do; return y end proc

proc (x, n, d) local i, y; y := Array(1 .. n); for i to n do y(i) := x(i)+d end do; return y end proc

(5)

"chost:=proc(p,q) local i,j,m; local Hpq,hh; Hpq:=Array(1..p+q-2); hh:=Array(1..p+q-2); for i from 1 to q-1 do Hpq(i):=i*p; od; for j from 1 to p-1 do; Hpq(i++):=j*q; od; hh:=sort(Hpq); return hh; end proc "

proc (p, q) local i, j, m, Hpq, hh; Hpq := Array(1 .. p+q-2); hh := Array(1 .. p+q-2); for i to q-1 do Hpq(i) := i*p end do; for j to p-1 do Hpq(`++`(i)) := j*q end do; hh := sort(Hpq); return hh end proc

(6)

nGroup := proc (p, m) local j, n, ar; ar := Array(1 .. m); for j from 0 to m-1 do n := ceil((j+1)*p/m)-floor(j*p/m)-1; ar(j+1) := n end do; return ar end proc

proc (p, m) local j, n, ar; ar := Array(1 .. m); for j from 0 to m-1 do n := ceil((j+1)*p/m)-floor(j*p/m)-1; ar(j+1) := n end do; return ar end proc

(7)

Position := proc (ary, k) local i, pos; pos := 0; for i to k-1 do pos := pos+ary(i) end do; pos := pos+1; return pos end proc

proc (ary, k) local i, pos; pos := 0; for i to k-1 do pos := pos+ary(i) end do; pos := pos+1; return pos end proc

(8)

$groups := proc (p, q, lm, m) local k, j, x, r, ll, rr, ni, bl, br, i; i := 1; printf("______\n"); for k from 0 to m-2 do ll := floor(k*p/m); rr := floor((k+1)*p/m); ni := rr-ll; for j to ni do r := (j+ll)*m-k*p; printf("(%d: %d),", i, r); if j = ni then printf(" # %d p-hosts after q-host %d\n", lm+1, i*q) end if; i := i+1 end do; printf("\n") end do; ll := floor((m-1)*p/m); rr := p-1; ni := rr-ll; for j to ni do r := (j+ll)*m-k*p; printf("(%d: %d),", i, r); i := i+1 end do; printf("\n______\n") end proc$

(9)

$idx := proc (p, m) local i, r, ri; for i to p-1 do r := i*m-floor(i*m/p)*p; if r = 1 or r = p-1 then ri := i end if; printf("%d, ", r) end do; printf("\n"); return ri end proc$

proc (p, m) local i, r, ri; for i to p-1 do r := i*m-floor(i*m/p)*p; if r = 1 or r = p-1 then ri := i end if; printf("%d, ", r) end do; printf("
"); return ri end proc

(10)

$DoTest := proc (p, q) local k, i, j, x, y, r, ni, lambda, n, g, xx, ll, rr, w, pos, nj, hh, grp; n := p+q-2; g := Array(1 .. n-1); hh := chost(p, q); printf("Hosts of p and q are:\n"); PrintArray(hh, n); lambda := floor(q/p); r := q-lambda*p; printf("Lambda=%d\nr=%d\n", lambda, r); printf("The %d elements in S(r,p) are:\n", p-1); for i to p-1 do printf("%d,", i*r) end do; printf("\n"); printf("The %d elements in rZ(r,p) are:\n", p-1); for j to p-1 do x := j*r-floor(j*r/p)*p; printf("%d,", x) end do; printf("\n"); printf("The %d subsets are as follows:\n", r); groups(p, q, lambda, r); printf("The maximum gap is: %d \n", p-1); g := q-p-1; printf("Total number of maximum gaps is:%d\n", g); g := GapArray(hh, n); xx := CopyArrayElem(hh, n-1); dataplot(xx, g) end proc$