OFFSET
1,2
COMMENTS
Write k as product of primes raised to powers; then a(n) is the least number k such that the total number of distinct digits in the product representation of k (number of distinct digits in all the primes and number of distinct digits in all the exponents that are greater than 1) is equal to n. The first term a(1)= 1 by convention. The sequence is complete.
Property: all exponents are equal to 1 (see the examples below).
EXAMPLE
a(1) = 1;
a(2) = 6 = 2*3 and A254315(6) = 2;
a(3) = 26 = 2*13 and A254315(26) = 3;
a(4) = 102 = 2*3*17 and A254315(102) = 4;
a(5) = 510 = 2*3*5*17 and A254315(510) = 5;
a(6) = 3210 = 2*3*5*107 and A254315(3210) = 6;
a(7) = 22890 = 2*3*5*7*109 and A254315(22890) = 7;
a(8) = 153690 = 2*3*5*47*109 and A254315(153690) = 8;
a(9) = 1507290 = 2*3*5*47*1069 and A254315(1507290) = 9;
a(10) = 15618090 = 2*3*5*487*1069 and A254315(15618090) = 10.
MAPLE
with(ListTools):
for n from 2 to 10 do:
ii:=0:
for k from 2 to 10^9 while(ii=0)do:
n0:=length(k):lst:={}:x0:=ifactors(k):
y:=Flatten(x0[2]):z:=convert(y, set):
z1:=z minus {1}:nn0:=nops(z1):
for m from 1 to nn0 do :
t1:=convert(z1[m], base, 10):z2:=convert(t1, set):
lst:=lst union z2:
od:
nn1:=nops(lst):
if nn1=n then ii:=1:printf ( "%d %d \n", n, k):
else
fi:
od :
od:
MATHEMATICA
f[n_] := Block[{pf = FactorInteger@ n, i}, Length@ DeleteDuplicates@ Flatten@ IntegerDigits@ Rest@ Flatten@ Reap@ Do[If[Last[pf[[i]]] == 1, Sow@ First@ pf[[i]], Sow@ FromDigits@ Flatten[IntegerDigits /@ pf[[i]]]], {i, Length@ pf}]]; b = -1; Flatten@ Last@ Reap@ Do[a = f[n]; If[a > b, Sow[n]; b = a], {n, 10^6}] (* Michael De Vlieger, Jan 29 2015 *)
With[{s = Array[CountDistinct@ Flatten@ IntegerDigits[FactorInteger[#] /. {p_, e_} /; e == 1 :> {p}] &, 10^6]}, Map[FirstPosition[s, #][[1]] &, Range@ Max@ s]] (* Michael De Vlieger, Nov 03 2017 *)
PROG
(PARI) a(n)=for(k=1, 10^5, s=[]; F=factor(k); for(i=1, #F[, 1], s=concat(s, digits(F[i, 1])); if(F[i, 2]>1, s=concat(s, digits(F[i, 2])))); if(#vecsort(s, , 8)==n, return(k)))
print1(1, ", "); for(n=2, 7, print1(a(n), ", ")) \\ Derek Orr, Jan 30 2015
CROSSREFS
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, Jan 28 2015
EXTENSIONS
a(10) corrected by Giovanni Resta, Nov 03 2017
STATUS
approved