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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).

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. [broken link]

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

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

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Last modified September 18 11:42 EDT 2018. Contains 315130 sequences. (Running on oeis4.)