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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).
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
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
Sequence in context: A267521 A202267 A125975 * A121232 A298746 A122428
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
More terms from Eric W. Weisstein
STATUS
approved

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Last modified April 13 17:26 EDT 2024. Contains 371644 sequences. (Running on oeis4.)