A046758 Equidigital numbers.

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

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).

The term "equidigital number" was coined by Recamán (1995). - Amiram Eldar, Mar 10 2024

References

Bernardo Recamán Santos, Equidigital representation: problem 2204, J. Rec. Math., Vol. 27, No. 1 (1995), pp. 58-59.

Links

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

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

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

Eric Weisstein's World of Mathematics, Equidigital Number..

Wikipedia, Equidigital number.

Formula

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

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, A055642, 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