A119738 Semiprimes that are semiprimes turned upside-down.

6, 9, 69, 106, 111, 119, 611, 669, 689, 698, 699, 818, 866, 869, 901, 998, 1011, 1101, 1111, 1198, 1199, 1661, 1681, 1689, 1691, 1819, 1891, 1919, 1961, 1966, 1991, 6009, 6019, 6109, 6119, 6161, 6181, 6189, 6611, 6686, 6819, 6866, 6889, 6891, 8186, 8611

Offset: 1

Author

Jonathan Vos Post, Jun 15 2006

Keywords

• nonn
• easy
• base

Examples

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

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• David A. Corneth, PARI program

Crossrefs

Cf. A000787, A001358, A045574.

Programs

Maple

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

Mathematica

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 *)

PARI

\\ See Corneth link. David A. Corneth, Sep 05 2020

Extensions

8186 inserted by R. J. Mathar, Sep 09 2008