login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046758 Equidigital numbers. 11
1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 105, 106, 107, 109, 111, 112, 113, 115, 118, 119, 121, 122, 123, 127, 129, 131, 133, 134, 135, 137, 139 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Write n as product of primes raised to powers, let D(n) = A050252 = total number of digits in product representation (number of digits in all the primes plus number of digits in all the exponents that are greater than 1) and l(n) = number of digits in n; sequence gives n such that D(n)=l(n).

A050252(a(n)) = A055642(a(n)). [Reinhard Zumkeller, Jun 21 2011]

LINKS

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

J. P. Delahaye, "Primes Hunters", Economical and Prodigal Numbers (Text in French) [broken link]

R. G. E. Pinch, Economical numbers, arXiv:math/9802046 [math.NT], 1998.

Eric Weisstein's World of Mathematics, Equidigital Number.

Wikipedia, Equidigital number

EXAMPLE

For n = 125 = 5^3, l(n) = 3 but D(n) = 2. So 125 is not a member of this sequence.

MATHEMATICA

edQ[n_] := Total[IntegerLength[DeleteCases[Flatten[FactorInteger[n]], 1]]] == IntegerLength[n]; Join[{1}, Select[Range[140], edQ]] (* Jayanta Basu, Jun 28 2013 *)

PROG

(Haskell)

a046758 n = a046758_list !! (n-1)

a046758_list = filter (\n -> a050252 n == a055642 n) [1..]

-- Reinhard Zumkeller, Jun 21 2011

(PARI) for(n=1, 100, s=""; F=factor(n); for(i=1, #F[, 1], s=concat(s, Str(F[i, 1])); s=concat(s, Str(F[i, 2]))); c=0; for(j=1, #F[, 2], if(F[j, 2]==1, c++)); if(#digits(n)==#s-c, print1(n, ", "))) \\ Derek Orr, Jan 30 2015

(Python)

from itertools import count, islice

from sympy import factorint

def A046758_gen(): # generator of terms

return (n for n in count(1) if n == 1 or len(str(n)) == sum(len(str(p))+(len(str(e)) if e > 1 else 0) for p, e in factorint(n).items()))

A046758_list = list(islice(A046758_gen(), 20)) # Chai Wah Wu, Feb 18 2022

CROSSREFS

Cf. A046759, A046760, A050252, A073048.

Sequence in context: A267521 A202267 A125975 * A121232 A298746 A122428

Adjacent sequences: A046755 A046756 A046757 * A046759 A046760 A046761

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Eric W. Weisstein

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 22:27 EST 2022. Contains 358671 sequences. (Running on oeis4.)