OFFSET
1,1
COMMENTS
Semiprime analog of A033274. If there is more than one digit, all digits must be nonsemiprime numbers {0,1,2,3,5,7,8}.
EXAMPLE
Start with all semiprimes and sieve out the ones which have semiprime substrings. Semiprime A001358(5) = 14 is not in this sequence because it contains the digit "4" which is semiprime A001358(1). Semiprime A001358(35) = 106 is not in this sequence because it contains the digit "6" which is semiprime A001358(2) and also contains as substring "10" which is semiprime A001358(4).
MAPLE
isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false ; fi ; end: Lton := proc(L) local a, i; a :=0 ; for i from 1 to nops(L) do a := 10*a+op(i, L) ; od: a ; end: isA137167 := proc(n) local dgs, strti, endi ; if isA001358(n) then dgs := ListTools[Reverse](convert(n, base, 10)) ; for strti from 1 to nops(dgs) do for endi from strti to nops(dgs) do if strti > 1 or endi < nops(dgs) then if isA001358(Lton([op(strti..endi, dgs)])) then RETURN(false) : fi ; fi ; od: od: RETURN(true) ; else RETURN(false) ; fi ; end: for n from 1 to 1600 do if isA137167(n) then printf("%d, ", n) ; fi ; od: # R. J. Mathar, Apr 12 2008
MATHEMATICA
smQ[n_]:=PrimeOmega[n]==2&&NoneTrue[Select[Union[FromDigits/@ Flatten[ Table[Partition[IntegerDigits[n], i, 1], {i, IntegerLength[n]-1}], 1]], #>0&], PrimeOmega[#]==2&]; Select[Range[1000], smQ] (* The program uses the NoneTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 26 2014 *)
CROSSREFS
KEYWORD
base,easy,nonn,less
AUTHOR
Jonathan Vos Post, Apr 03 2008
EXTENSIONS
More terms from R. J. Mathar, Apr 12 2008
STATUS
approved