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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 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

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