

A241946


Numbers n equal to the sum of all the fourdigit numbers formed without repetition from the digits of n.


2



1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443, 3553, 3663, 3773, 3883, 3993, 4004, 4114, 4224, 4334, 4444, 4554, 4664, 4774, 4884, 4994, 5005, 5115, 5225
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OFFSET

1,1


COMMENTS

Let d(1)d(2)... d(q) denote the decimal expansion of a number n. Any decimal expansion of fourdigits d(i)d(j)d(k)d(l) formed from the digits of n is such that i<j<k<l or i>j>k>l.
This sequence is interesting because it contains more than just the only trivial palindromic values 1001, 1111, 1221,... The sequence is given by the union of subsets {palindromes with four digits from A056524} union {37323, 48015, 72468, 152658} and contains 94 elements. The last four elements are nonpalindromic numbers.
But the generalization of this problem seems difficult, for example the case with the sum of all the threedigit numbers formed without repetition from the digits of n gives only 90 palindromic numbers 101, 111, 121,..., 989,999.


LINKS



EXAMPLE

37323 is in the sequence because 37323 = 2373 + 3233 + 3237 + 3273 + 3323 + 3373 + 3723 + 3732 + 3733 + 7323.


MAPLE

with(numtheory):
for n from 1000 to 10000 do:
lst:={}:k:=0:x:=convert(n, base, 10):n1:=nops(x):
for i from 1 to n1 do:
for j from i+1 to n1 do:
for m from j+1 to n1 do:
for q from m+1 to n1 do:
lst:=lst union {x[i]+10*x[j]+100*x[m]+1000*x[q]}:
od:
od:
od:
od:
for a from n1 by 1 to 1 do:
for b from a1 by 1 to 1 do:
for c from b1 by 1 to 1 do:
for d from c1 by 1 to 1 do:
lst:=lst union
{x[a]+10*x[b]+100*x[c]+1000*x[d]}:
od:
od:
od:
od:
n2:=nops(lst):s:=sum('lst[i]', 'i'=1..n2):
if s=n
then
printf(`%d, `, n):
else
fi:
od:


CROSSREFS



KEYWORD

nonn,base,fini,full


AUTHOR



STATUS

approved



