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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.
0
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.
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
Sequence in context: A045815 A182294 A103912 * A269279 A234552 A223466
KEYWORD
nonn,base,fini,full,bref
AUTHOR
Michel Lagneau, Mar 14 2015
STATUS
approved