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 A054841 If n = 2^a * 3^b * 5^c * 7^d * ... then a(n) = a + 10 * b + 100 * c + 1000 * d + ... . 27
 0, 1, 10, 2, 100, 11, 1000, 3, 20, 101, 10000, 12, 100000, 1001, 110, 4, 1000000, 21, 10000000, 102, 1010, 10001, 100000000, 13, 200, 100001, 30, 1002, 1000000000, 111, 10000000000, 5, 10010, 1000001, 1100, 22, 100000000000, 10000001, 100010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Are there any other numbers besides n=12 for which n=a(n) ? - Ctibor O. Zizka, Oct 08 2008 The sequence is a morphism from (N*,*) into (N,+), cf. formula. Up to n=1023, the digit sum A007953(a(n)) equals Omega(n) = A001222(n). This holds whenever A051903(n)<10. Restricted to these n, the sequence is also injective. However, when n is a multiple of 2^10, 3^10, 5^10 etc, then a(n) is equal to some a(m) with m 10 would be used). - M. F. Hasler, Jul 03 2016 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 (n=1..1023 from Michael De Vlieger) Evans A Criswell, A Sequence Puzzle (Posted to rec.puzzles Jan 01 1997) Walter Nissen, Exponential Prime Power Representation, sci.math newsgroup, May 23 1995. FORMULA a(m*n) = a(m) + a(n) for all m,n > 0. A007953(a(n))=A001222(n) for all n such that A051903(n) < 10. - M. F. Hasler, Nov 16 2008 a(n) = sum(10^(A049084(A027748(k))-1) * A124010(k): k = 1..A001221(n)). - Reinhard Zumkeller, Aug 03 2015 a(A054842(n)) = n for all n >= 0. - Antti Karttunen, Aug 29 2016 a(n) = Sum_{i>0} e_i*10^(i-1) when n = Product_{i>0} prime(i)^e_i. - M. F. Hasler, Mar 14 2018 EXAMPLE a(25) = 200 because 25 = 5^2 * 3^0 * 2^0. a(1024) = 10 = a(3), because 1024 = 2^10; but this two-digit multiplicity overflows into the 10^1 position, which encodes for powers of three. MAPLE A:= n -> add(t[2]*10^(numtheory:-pi(t[1])-1), t= ifactors(n)[2]); seq(A(n), n=1..1000); # Robert Israel, Jul 24 2014 MATHEMATICA a054841[n_Integer] := Catch[FromDigits[IntegerDigits[Apply[Plus,      Which[n == 0, Throw["undefined"],         n == 1, 0,         Max[Last /@ FactorInteger @ n] > 9, Throw["overflow"],         True, Power[10, PrimePi[Abs[#]] - 1]] & /@       Flatten[ConstantArray @@@ FactorInteger[n]]]]]] (* Michael De Vlieger, Jul 24 2014 *) PROG (PARI) A054841(n)=sum(i=1, #n=factor(n)~, 10^primepi(n[1, i])*n[2, i])/10 \\ M. F. Hasler, Nov 16 2008 (Haskell) a054841 1 = 0 a054841 n = sum \$ zipWith (*)                   (map ((10 ^) . subtract 1 . a049084) \$ a027748_row n)                   (map fromIntegral \$ a124010_row n) -- Reinhard Zumkeller, Aug 03 2015 CROSSREFS Row 10 of A104244. Left inverse of A054842. Cf. A001222, A048675, A090880, A090881, A090882, A276075, A276085 (analogous constructions for other bases), A090883, A090884, A049084, A027748, A124010, A056239. Sequence in context: A305995 A096043 A001202 * A185076 A178643 A038304 Adjacent sequences:  A054838 A054839 A054840 * A054842 A054843 A054844 KEYWORD base,nonn AUTHOR Henry Bottomley, Apr 11 2000 STATUS approved

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Last modified June 2 11:20 EDT 2020. Contains 334771 sequences. (Running on oeis4.)