<div>There must be an elegant expression in Mathematica for the general case of base k emirpimes.</div>
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<div>For base 5, the analogous sequence begins 14, 24, 41, 42, 114, 123, 124, 144, 213, 244, ...</div>
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<div>And which integers are emirpimes in more than one base? More than two?</div>
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<div>In one sense, these are all silly. In another, A097393 was my first sequence. There is plenty of usage of digital reversal in OEIS. It has deeper meaning when we look at reversals of strings of operators. For example, for the adjoint operator usually denoted with a superscripted dagger and a set of adjoint operators A, B, ..., Z, we have:
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<div>(AB...Z)^dagger = Z^dagger ... B^dagger A^dagger.</div>
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<div><a href="http://mathworld.wolfram.com/about/author.html">Weisstein, Eric W.</a> "Adjoint." From <a href="http://mathworld.wolfram.com/"><i>MathWorld</i></a>--A Wolfram Web Resource. <a href="http://mathworld.wolfram.com/Adjoint.html">
http://mathworld.wolfram.com/Adjoint.html</a> </div>
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<div>%I A000001<br>%S A000001 12, 21, 1022, 1113, 1222, 1233, 1303, 1313, 1323, 2011, <br>2012, 2032, 2102, 2201, 2221, 2302, 3031, 3111, 3131, 3231<br>%N A000001 Quaternary emirpimes.<br>%C A000001 These are semiprimes when read as base 4 numbers, and their
<br>reversals are different semiprimes when read as base 4 numbers. Base 4 <br>analogue of what for base 3 is A119684 and for base 10 is A097393. The <br>base 10 representation of this sequence is: 6, 9, 74, 87, 106, 111,
<br>115, 119, 123, 133, 134, 142, 146, 161, 169, 178, 205, 213, 221, 237.<br>%H A000001 Eric W. Weisstein, Jonathan Vos Post, et al., <a <br>href="<a href="http://mathworld.wolfram.com/Emirpimes.html" target="_blank">
<font color="#003399">http://mathworld.wolfram.com/Emirpimes.html</font></a>">Emirpimes</a>.<br>%H A000001 Eric W. Weisstein, <a <br>href="<a href="http://mathworld.wolfram.com/Quaternary.html" target="_blank">
<font color="#003399">http://mathworld.wolfram.com/Quaternary.html</font></a>">Quaternary</a>.<br>%F A000001 a(n) = A007090(i) for some i in A001358, and R(a(n)) = <br>A007090(j) for some j =/= i in A001358. a(n) = A007090(i) for some i in
<br>A001358, and A004086(a(n)) = A007090(j) for some j =/= i in A001358.<br>%e A000001 a(1) = 12 because 12 (base 4) = 6 (base 10) is semiprime, <br>and R(12) = 21, where 21 (base 4) = 9 (base 10) is a different semiprime.
<br>a(19) = 3131 because 3131 (base 4) = 221 (base 10) = 13 * 17 (base 10) <br>is semiprime, and R(3131) = 1313, where 1313 (base 4) = 119 (base 10) = <br>7 * 17 (base 10) is a different semiprime.<br>%Y A000001 Cf. A001358, A004086, A007090, A097393.
<br>%O A000001 1<br>%K A000001 ,base,easy,nonn,<br>%A A000001 Jonathan Vos Post (<a href="http://us.f365.mail.yahoo.com/ym/Compose?To=jvospost2@yahoo.com&YY=94896&order=down&sort=date&pos=0&view=a&head=b">
<font color="#003399">jvospost2@yahoo.com</font></a>), Jun 13 2006<br> </div>