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A046759 Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n). 10
125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875, 2048, 2187, 2197, 2209, 2401, 2560, 2809, 3125, 3481, 3584, 3645, 3721, 4096, 4374, 4375, 4489, 4802, 4913 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A050252(a(n)) < A055642(a(n)). - Reinhard Zumkeller, Jun 21 2011

LINKS

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

C. K. Caldwell, The Prime Glossary, economical number

J.-M. De Koninck and F. Luca, On strings of consecutive economical numbers of arbitrary length

J.-P. Delahaye, Les chasseurs de nombres premiers

R. G. E. Pinch, Economical numbers

R. G. E. Pinch, Economical numbers

W. Schneider, Economical Numbers

G. Villemin's Almanach of Numbers, Nombres Economes

Eric Weisstein's World of Mathematics, Economical Number.

Wikipedia, Frugal number

EXAMPLE

For n = 125 = 5^3, l(n) = 3 but D(n) = 2.

MATHEMATICA

ecoQ[n_] := Total[ Length /@ IntegerDigits /@ Flatten[ FactorInteger[n] /. {p_, 1} -> p]] < Length[ IntegerDigits[n]]; Select[ Range[5000], ecoQ] (* Jean-Fran├žois Alcover, Jul 28 2011 *)

PROG

(Haskell)

a046759 n = a046759_list !! (n-1)

a046759_list = filter (\n -> a050252 n < a055642 n) [1..]

-- Reinhard Zumkeller, Jun 21 2011

(PARI) is(n)=my(f=factor(n)); sum(i=1, #f[, 1], #Str(f[i, 1])+if(f[i, 2]>1, #Str(f[i, 2])))<#Str(n) && n>1 \\ Charles R Greathouse IV, Feb 01 2013

CROSSREFS

Cf. A046758, A046760.

Sequence in context: A195420 A080538 A104233 * A115938 A126895 A202240

Adjacent sequences:  A046756 A046757 A046758 * A046760 A046761 A046762

KEYWORD

nonn,nice,base

AUTHOR

N. J. A. Sloane, Dec 11 1999

EXTENSIONS

More terms from Eric W. Weisstein

STATUS

approved

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Last modified November 26 13:05 EST 2014. Contains 250079 sequences.