A256104 Differential autobiographical numbers: number n = x0 x1 x2 ... x9 such that xi is the number of pairs (xj, xk), j different from k, where |xj - xk| = i.

20404, 31330

Offset

1,1

Comments

The first digit specifies how many |xj - xk| = 0 in the number, the next digit specifies how many |xj - xk| = 1, etc.

Links

Table of n, a(n) for n=1..2.

Example

31330 is in the sequence because:
|x0 - x2| = 0, |x0 - x3| = 0 and |x2 - x3| = 0 => x0 = 3;
|x1 - x3| = 1 => x1 = 1;
|x0 - x1| = 2, |x1 - x2| = 2 and |x1 - x3| = 2 => x2 = 3;
|x0 - x4| = 3, |x2 - x4| = 3 and |x3 - x4| = 3 => x2 = 3;
|xj - xk| = 4 does not occur for all j and k => x4 = 0.

Maple

for n from  10 to 10^10 do:
  x:=convert(n, base, 10):n0:=nops(x):T:=array(0..9):
    for a from 0 to 9 do:
    T[a]:=0:
    od:
     for i from 0 to 9 do:
      for j from 1 to n0-1 do:
       for k from j+1 to n0 do:
       if abs(x[j]-x[k])= i
       then
       T[i]:=T[i]+1:
       else
       fi:
     od:
    od:
   od:
    s:=sum('T[m]*10^(n0-m-1)', 'm'=0..9):
    if s=n then print(n) else fi:od:

Crossrefs

Cf. A046043, A234512.

Sequence in context: A045815 A182294 A103912 * A269279 A234552 A223466

Adjacent sequences: A256101 A256102 A256103 * A256105 A256106 A256107

Keyword

nonn,base,fini,full,bref

Author

Michel Lagneau, Mar 14 2015

Status

approved