# Support program for the conjecture

Jan 3rd, 2013
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1. /* Original code for A055881 by: Joerg Arndt (www.jjj.de) Dec 2012
2.  Sequencer adaptation for A196020 by: R. J. Cano, ( aallggoorriitthhmmuuss_at_gmail.com ), Jan 2013 */
3. first_diff_mode=0;
4. base=10;
5. n=10; \\  Warning: n should not be greater than 10... never, if all computations are assumed in base-10;
6. fc=vector(n) /* mixed radix numbers (rising factorial base) */
7. ct=0; a=0; p=vector(n,k,k-1) /* permutation */
8. t=0; j=0; w=#p; G=sum(y=1,w,p[y]*base^(w-y));
9. updater()=
10. {
11.         ct += 1;
12.         /* increment factorial number fc[]: */
13.         j = 1;
14.         while ( fc[j] == j,  fc[j]=0;  j+=1; );  /* scan over nines */
15.         if ( j==n,  return() );  /* current is last */
16.         fc[j] += 1;
17.         /* update permutation p[], reverse prefix of length j+1: */
18.         a = j;  /* next term of A055881 */
19.         j += 1;  k = 1;
20.         while ( k < j,
21.             t=p[j]; p[j]=p[k]; p[k]=t;
22.             k+=1; j-=1;
23.         );
24.     H=sum(y=1,w,p[y]*base^(w-y));
25.         ans=(H-G)\(base-1);
26.         if(first_diff_mode,G=H);
27.     /* */
28.     Qq=0;
29.     while(ans%base==0, ans/=base; Qq++); \\ Useful for the checking of the "((p-1)!-1) Conjecture".
30.         \\ Below return either ans or Qq depending of the attribute you want to know for a(n): The coefficient or the power.
31.     /* * /
32.         ans;
33.     / * */I
34.     /**/
35.         Qq;  \\ Before enabling this, ensure that first_diff_mode is set to zero!.
36.     /**/
37. }
38. if(!first_diff_mode, print("0")); for(u=1,(n!-1),print(updater()));
39. quit;