A241899 Numbers n equal to the sum of all the two-digit numbers formed without repetition from the digits of n.

11, 22, 33, 44, 55, 66, 77, 88, 99, 132, 264, 396

Offset: 10

Author

Michel Lagneau, May 01 2014

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is complete because the maximum number of partitions of an m-digit number n into sets of 2-digit numbers is 2*binomial(m,2) = m*(m-1). (See the Oblong numbers A002378.) The maximum value of the sum of all the two-digit numbers is M = 99*m*(m-1) where m = floor(log_10(n) + 1). But M < n for n > 1188 because the solution of the equation 99*m*(m-1) = n with m = floor(log_10(n) + 1) is n = 1188.

Examples

			132 is in the sequence because 132 = 12 + 13 + 21 + 23 + 31 + 32.
		

Crossrefs

Cf. A002378.

Programs

Maple

with(numtheory):
for n from 10 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:
          lst:=lst union {x[i]+10*x[j]}:
          od:
        od:
           for a from n1 by -1 to 1 do:
             for b from a-1 by -1 to 1 do:
             lst:=lst union
             {x[a]+10*x[b]}:
             od:
           od:
           n2:=nops(lst):s:=sum('lst[i]', 'i'=1..n2):
           if s=n
             then
             printf(`%d, `,n):
             else
           fi:
  od:

Mathematica

Select[Range[10,400],Total[FromDigits/@Permutations[IntegerDigits[#],{2}]]==#&] (* Ivan N. Ianakiev, Oct 24 2014 *)