A114015 - OEIS

%I #14 Aug 09 2015 00:25:29

%S 12,21,1022,1102,1113,1222,1233,1303,1313,1323,2011,2012,2032,2102,

%T 2201,2221,2302,3031,3111,3131,3231,3321,10102,10213,10231,10232,

%U 10233,10322,11012,11033,11103,11231,11321,11331,12013,12022,12023,12032

%N Quaternary emirpimes.

%C These are semiprimes when read as base-4 numbers and their reversals are different semiprimes when read as base-4 numbers. Base-4 analog of what for base 3 is A119684 and for base 10 is A097393. The base-10 representation of this sequence is 6, 9, 74, 87, 106, 111, 115, 119, 123, 133, 134, 142, 146, 161, 169, 178, 205, 213, 221, 237.

%H Eric Weisstein, Jonathan Vos Post, et al., <a href="http://mathworld.wolfram.com/Emirpimes.html">Emirpimes</a>.

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

%F a(n) = A007090(i) for some i in A001358 and R(a(n)) = A007090(j) for some j =/= i in A001358. a(n) = A007090(i) for some i in A001358 and A004086(a(n)) = A007090(j) for some j =/= i in A001358.

%e a(1) = 12 because 12 (base 4) = 6 (base 10) is semiprime and R(12) = 21, where 21 (base 4) = 9 (base 10) is a different semiprime.

%e a(19) = 3131 because 3131 (base 4) = 221 (base 10) = 13 * 17 (base 10) is semiprime and R(3131) = 1313, where 1313 (base 4) = 119 (base 10) = 7 * 17 (base 10) is a different semiprime.

%p A007090 := proc(n) local b4; b4 := convert(n,base,4) ; add( op(i,b4)*10^(i-1),i=1..nops(b4)) ; end proc:

%p isA114015 := proc(n) local b4;b4rev; if isA001358(n) then b4 := convert(n,base,4) ; b4rev := add(op(-i,b4)*4^(i-1),i=1..nops(b4)) ; if n = b4rev then false; else isA001358(b4rev) ; end if; else false; end if; end proc:

%p for n from 1 to 400 do if isA114015(n) then printf("%d,",A007090(n)) ; end if; end do: # _R. J. Mathar_, Dec 22 2010

%Y Cf. A001358, A004086, A007090, A097393.

%K base,easy,nonn,less

%O 1,1

%A _Jonathan Vos Post_, Jun 13 2006

%E 1102 inserted by _R. J. Mathar_, Dec 22 2010