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A161594 a(n) = R(f(n)), where f(n) = A071786(n), R(n) = A004086(n). 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 21, 13, 41, 51, 61, 17, 81, 19, 2, 12, 22, 23, 42, 52, 26, 72, 82, 29, 3, 31, 23, 33, 241, 53, 63, 37, 281, 39, 4, 41, 24, 43, 44, 54, 46, 47, 84, 94, 5, 312, 421, 53, 45, 55, 65, 372, 481, 59, 6, 61, 62, 36, 46, 551, 66, 67, 482, 69, 7, 71, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Might be called TITO(n), turning n inside out then turning outside in.

Here is the operation: take a number n and find its prime factors. Reverse the digits of every prime factor (for example, replace 17 by 71). Multiply the factors respecting multiplicities. For example, if the original number was 17^2*43^3, the new product will be 71^2*34^3. After that, reverse the resulting number.

a(A161598(n)) <> A161598(n); a(A161597(n)) = A161597(n); A010051(a(A161600(n))) = 1.

LINKS

M. F. Hasler, Table of n, a(n) for n=1,...,5000. [From M. F. Hasler, Jun 24 2009]

T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova, Jul 07 2009]

FORMULA

a(p) = p, for prime p.

Comment from M. F. Hasler, Jun 25 2009: a( p*10^k ) = p for any prime p.

Proof: * if gcd( p, 2*5) = 1, then a( p * 10^k ) = R( R(p) * R(2)^k * R(5)^k ) = R( R(p) * 10^k ) = R( R(p)) = p

* if gcd( p, 2*5) = 2, then p=2 and a( p * 10^k ) = R( R(2)^(k+1) * R(5)^k ) = R( 2 * 10^k ) = 2 = p and mutatis mutandis for gcd( p, 2*5) = 5.

EXAMPLE

a(34) = 241, because 34 = 2*17, f(34) = 2*71 = 142, and reversing gives 241.

MAPLE

read("transforms") ; A071786 := proc(n) local ifs, a, d ; ifs := ifactors(n)[2] ; a := 1 ; for d in ifs do a := a*digrev(op(1, d))^op(2, d) ; od: a ; end: A161594 := proc(n) digrev(A071786(n)) ; end: seq(A161594(n), n=1..80) ; [From R. J. Mathar, Jun 16 2009]

MATHEMATICA

reversepower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n]]]^k f[n_] := FromDigits[ Reverse[IntegerDigits[Times @@ Map[reversepower, FactorInteger[n]]]]] Table[f[n], {n, 100}]

PROG

Contribution from M. F. Hasler, Jun 24 2009: (Start)

(PARI) A161594(n)={n=factor(n); n[, 1]=apply(R, n[, 1]); R(factorback(n))}

R(n)=eval(concat(vecextract(Vec(Str(n)), "-1..1"))) /* = A004086(n) */ (End)

(Haskell)

a161594 = a004086 . a071786  -- Reinhard Zumkeller, Oct 14 2011

CROSSREFS

Cf. A161597, A161598, A161600, A071786, A004086, A151764.

Sequence in context: A004151 A151765 A107603 * A084011 A004086 A121760

Adjacent sequences:  A161591 A161592 A161593 * A161595 A161596 A161597

KEYWORD

nonn,base,nice,look

AUTHOR

J. H. Conway & Tanya Khovanova, Jun 14 2009

EXTENSIONS

Simpler definition from R. J. Mathar, Jun 16 2009

Edited by N. J. A. Sloane, Jun 23 2009

STATUS

approved

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Last modified September 1 22:15 EDT 2014. Contains 246317 sequences.