OFFSET
10,1
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.
EXAMPLE
132 is in the sequence because 132 = 12 + 13 + 21 + 23 + 31 + 32.
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 *)
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, May 01 2014
STATUS
approved