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A119738
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Semiprimes that are semiprimes turned upside-down.
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1
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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
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OFFSET
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1,1
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COMMENTS
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This sequence has, as a subset, strobogrammatic semiprimes = A000787 INTERSECTION A001358 = {69, 111, 689, 818, 1111, 1691, 1961, 6009, 6119, 6889, 8698, 9886, 10001, 10801, 11111, ...} including the strobogrammatic square 6889 = 83^2. See also A045574 Still numbers when turned upside down (uses only digits 0, 1, 6, 8, 9 with no final 0's). A000787 Strobogrammatic numbers: the same upside down.
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LINKS
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FORMULA
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a(n) in A001358, a(n) =/= 10 and a(n) upside-down in A001358. UpsideDown(k) is R(k) followed by the substitutions (0,0), (1,1), (6,9), (8,8), (9,6).
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EXAMPLE
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19606 = 2 * 9803 upside-down is 90961 = 13 * 6997.
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MAPLE
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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
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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