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A241946 Numbers n equal to the sum of all the four-digit 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let d(1)d(2)... d(q) denote the decimal expansion of a number n. Any decimal expansion of four-digits 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 non-palindromic numbers.

But the generalization of this problem seems difficult, for example the case with the sum of all the three-digit numbers formed without repetition from the digits of n gives only 90 palindromic numbers 101, 111, 121,..., 989,999.

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..93

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 a-1 by -1 to 1 do:

               for c from b-1 by -1 to 1 do:

                 for d from c-1 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

Cf. A241899.

Sequence in context: A044881 A291269 A317291 * A100846 A153814 A259080

Adjacent sequences:  A241943 A241944 A241945 * A241947 A241948 A241949

KEYWORD

nonn,base,fini,full

AUTHOR

Michel Lagneau, May 03 2014

STATUS

approved

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)