A119738 - OEIS

%I #24 Sep 19 2024 12:25:25

%S 6,9,69,106,111,119,611,669,689,698,699,818,866,869,901,998,1011,1101,

%T 1111,1198,1199,1661,1681,1689,1691,1819,1891,1919,1961,1966,1991,

%U 6009,6019,6109,6119,6161,6181,6189,6611,6686,6819,6866,6889,6891,8186,8611

%N Semiprimes that are semiprimes turned upside-down.

%H David A. Corneth, <a href="/A119738/b119738.txt">Table of n, a(n) for n = 1..10000</a>

%H David A. Corneth, <a href="/A119738/a119738.gp.txt">PARI program</a>

%e 19606 = 2 * 9803 upside-down is 90961 = 13 * 6997.

%p UpsideDown := proc(n) local dgs,a,i ; dgs := convert(n,base,10) ; a := [] ; for i from 1 to nops(dgs) do if op(i,dgs) = 6 then a := [9,op(a)] ; elif op(i,dgs) = 9 then a := [6,op(a)] ; else a := [op(i,dgs),op(a)] ; fi; od: add(op(i,a)*10^(i-1),i=1..nops(a)) ; end: isA054047 := proc(n) local dgs,i ; dgs := convert(n,base,10) ; for i from 1 to nops(dgs) do if not op(i,dgs) in {0,1,6,8,9} then RETURN(false) : fi; od: RETURN(true) ; end: isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true; else false; fi; end: isA119738 := proc(n) if isA001358(n) and isA054047(n) then isA001358(UpsideDown(n)) ; else false ; fi; end: for n from 1 to 12000 do if isA119738(n) then printf("%a,",n) ; fi; od: # _R. J. Mathar_, Sep 09 2008

%t Select[Range[8611],ContainsOnly[IntegerDigits[#],{0,1,6,8,9}]&&PrimeOmega[#]==2&&PrimeOmega[FromDigits[Reverse[IntegerDigits[#]]/.{6->9,9->6}]]==2&] (* _James C. McMahon_, Sep 18 2024 *)

%o (PARI) \\ See Corneth link. _David A. Corneth_, Sep 05 2020

%Y Cf. A000787, A001358, A045574.

%K nonn,easy,base

%O 1,1

%A _Jonathan Vos Post_, Jun 15 2006

%E 8186 inserted by _R. J. Mathar_, Sep 09 2008