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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.

%I A256104 #9 Mar 18 2015 06:03:22
%S A256104 20404,31330
%N 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.
%C A256104 The first digit specifies how many |xj - xk| = 0 in the number, the next digit specifies how many |xj - xk| = 1, etc.
%e A256104 31330 is in the sequence because:
%e A256104 |x0 - x2| = 0, |x0 - x3| = 0 and |x2 - x3| = 0 => x0 = 3;
%e A256104 |x1 - x3| = 1 => x1 = 1;
%e A256104 |x0 - x1| = 2, |x1 - x2| = 2 and |x1 - x3| = 2 => x2 = 3;
%e A256104 |x0 - x4| = 3, |x2 - x4| = 3 and |x3 - x4| = 3 => x2 = 3;
%e A256104 |xj - xk| = 4 does not occur for all j and k => x4 = 0.
%p A256104 for n from  10 to 10^10 do:
%p A256104   x:=convert(n,base,10):n0:=nops(x):T:=array(0..9):
%p A256104     for a from 0 to 9 do:
%p A256104     T[a]:=0:
%p A256104     od:
%p A256104      for i from 0 to 9 do:
%p A256104       for j from 1 to n0-1 do:
%p A256104        for k from j+1 to n0 do:
%p A256104        if abs(x[j]-x[k])= i
%p A256104        then
%p A256104        T[i]:=T[i]+1:
%p A256104        else
%p A256104        fi:
%p A256104      od:
%p A256104     od:
%p A256104    od:
%p A256104     s:=sum('T[m]*10^(n0-m-1)', 'm'=0..9):
%p A256104     if s=n then print(n) else fi:od:
%Y A256104 Cf. A046043, A234512.
%K A256104 nonn,base,fini,full,bref
%O A256104 1,1
%A A256104 _Michel Lagneau_, Mar 14 2015