A073646 Least number formed by concatenating the prime factors of n in base 10.

1, 2, 3, 22, 5, 23, 7, 222, 33, 25, 11, 223, 13, 27, 35, 2222, 17, 233, 19, 225, 37, 112, 23, 2223, 55, 132, 333, 227, 29, 235, 31, 22222, 113, 172, 57, 2233, 37, 192, 133, 2225, 41, 237, 43, 1122, 335, 223, 47, 22223, 77, 255, 173, 1322, 53, 2333, 115, 2227

Offset

1,2

Comments

a(n)<=A037276(n) for all n and a(n)=A037276(n) for n<22, a(22) = a(2*11) = 112 <> A037276(22) = 211.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

Sort {A027746(n,k): k=1..A001222(n)} lexicographically and concatenate. - Reinhard Zumkeller, Jul 13 2013

Example

a(6) = a(2*3) = 23 < 32; a(66) = a(2*3*11) = 1123 < 1132 < 2113 < 2311 < 3112 < 3211.

Mathematica

con[n_, k_] := Nest[Join[{#}, {n}] &, n, k - 1]; Table[Min[FromDigits /@ Flatten /@ IntegerDigits[Permutations[Flatten[con @@@ FactorInteger[n]]]]], {n, 56}] (* Jayanta Basu, Jul 04 2013 *)

Prog

(Haskell)
import Data.List (sort)
a073646 :: Integer -> Integer
a073646 = read . concat . sort . map show . a027746_row
-- Reinhard Zumkeller, Jul 13 2013

Crossrefs

Different from A037276. Cf. A084797.

Sequence in context: A080670 A288532 A073647 * A037276 A068190 A084796

Adjacent sequences: A073643 A073644 A073645 * A073647 A073648 A073649

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Aug 29 2002

Status

approved