OFFSET
1,1
COMMENTS
The number of concatenations is d(x)-1, where d(x) is the number of divisors of x (z = concat(z) is excluded).
EXAMPLE
z = 1488, x = 4. The concatenations are (1,4,8,8), (14,88) and f(z) = 1*4*8*8 + 14*88 = 1488 (fixed point).
z = 165864, x = 6. The concatenations are (1,6,5,8,6,4), (16,58,64), (165,864) and f(z) = 1*6*5*8*6*4 + 16*58*64 + 165*864 = 207712.
Now, z = 207712, x = 6. The concatenations are (2,0,7,7,1,2), (20,77,12), (207,712) and f(z) = 2*0*7*7*1*2 + 20*77*12 + 207*712 = 165864.
Therefore both 165864 and 207712 are terms of the sequence.
MAPLE
with(numtheory): T:=proc(w) local i, k, x, y, z; z:=0; i:=sort([op(divisors(ilog10(w)+1))]); for k from 1 to nops(i)-1 do x:=1; y:=w; while y>0 do x:=x*(y mod 10^i[k]); y:=trunc(y/10^i[k]); od; z:=z+x; od; z; end:P:=proc(q) local c, d, j, n; for j from 1 to q do if not isprime(j+1) then for n from 10^j to 10^(j+1)-1 do c:=T(n); if c>0 then d:=T(c); fi; if d=n then print(n); fi; od; fi; od; end: P(10^9);
MATHEMATICA
f[n_] := With[{w = IntegerDigits@ n}, Total@ Flatten@ Map[Times @@ Map[FromDigits, Partition[w, #, #]] &, Most@ Divisors@ Length@ w]]; Select[Range[10^6], f@ f@ # == # &] (* Michael De Vlieger, Aug 05 2018 *)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Paolo P. Lava, Aug 01 2018
EXTENSIONS
a(16)-a(27) from Giovanni Resta, Aug 01 2018
STATUS
approved