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A097393 Emirpimes: numbers n such that n and its reversal are distinct semiprimes. 30

%I #26 Jan 07 2024 07:33:39

%S 15,26,39,49,51,58,62,85,93,94,115,122,123,129,143,155,158,159,169,

%T 177,178,183,185,187,203,205,221,226,265,289,302,314,319,321,326,327,

%U 329,335,339,341,355,381,394,398,413,415,437,493,497,502,511,514,533

%N Emirpimes: numbers n such that n and its reversal are distinct semiprimes.

%C Computed by _Eric W. Weisstein_, Aug 13 2004.

%H Charles R Greathouse IV, <a href="/A097393/b097393.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Emirpimes.html">Emirpimes</a>

%e 26 is a semiprime, as it is 2 * 13, and so is 62 = 2 * 31. 26 and 62 are therefore both in the sequence.

%p isA097393 := proc(n)

%p local R ;

%p R := digrev(n) ;

%p if R <> n then

%p if numtheory[bigomega](R) = 2 and numtheory[bigomega](n) = 2 then

%p return true;

%p else

%p false;

%p end if;

%p else

%p false;

%p end if;

%p end proc:

%p for n from 1 to 500 do

%p if isA097393(n) then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Apr 05 2012

%t Cases[{#, IntegerReverse@#} & /@ DeleteCases[Range@5000, _?PalindromeQ], {_?(PrimeOmega@# == 2 &) ..}][[All,1]] (* _Hans Rudolf Widmer_, Jan 07 2024 *)

%o (PARI) rev(n)=subst(Polrev(digits(n)),'x,10)

%o issemi(n)=bigomega(n)==2

%o list(lim)=my(v=List(),r);forprime(p=2,lim\2,forprime(q=2,min(lim\p,p),r=rev(p*q);if(issemi(r)&&r!=p*q,listput(v,p*q))));Set(v) \\ _Charles R Greathouse IV_, Jan 27 2015

%o (Python)

%o from sympy import factorint

%o from itertools import islice

%o def sp(n): f = factorint(n); return sum(f[p] for p in f) == 2

%o def ok(n): r = int(str(n)[::-1]); return r != n and sp(n) and sp(r)

%o print([k for k in range(534) if ok(k)]) # _Michael S. Branicky_, Jul 03 2022

%Y Cf. A001358, A097394.

%Y Equals A085751 \ A046328.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)