
COMMENTS

ds(m) is the number that is obtained from m by replacing each positive digit i to sigma(i) and replacing zero by zero itself.
Example: ds(19)=1.13=113, ds(1028)=1.0.3.15=10315.
1. If all digits of m are less than 2 then ds(m)=m. So for
primes p with digits less than 2 (terms of the sequence A020449) p=ds(p)=ds(ds(p))=ds(ds(ds(p)))= ... .
2. For n>1, a(n) is of the form 10k+1.
3. If o, i, s and t are respectively number of zeros, number of ones, number of digits greater than 1 and number of composite digits greater than 4 in decimal expansion of m also o', i', s' and t' are the same for ds(m) then o'=o, i'=i+t and s'=s.
Example: m=1021041629839
ds(m)=1.0.3.1.0.7.1.12.3.13.15.4.13=10310711231315413
=> {o, i, s, t}={2, 3, 8, 4} and {o', i', s'}={o, i+t, s}= {2, 7, 8}.
