OFFSET
1,1
COMMENTS
Semiprime analog of A030284.
EXAMPLE
The first 4 values are the first 4 semiprimes. But, following 10, we cannot have 14, 15, or 21 (any of the next 3 semiprimes) because they all share the digit 1 with 10. Hence a(5) = 22. The sequence is infinite, as with the prime analog. Sketch of proof: obviously true unless we hit a pandigital semiprime (with all 10 digits used), after which no base 10 integer can follow. Such semiprimes exist, the smallest being 10123456789. But we cannot have such a value in this sequence, as it violates the definition.
MAPLE
isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false ; fi ; end: sharedDgs := proc(a, b) local adigs, bdigs ; adigs := convert(convert(a, base, 10), set) ; bdigs := convert(convert(b, base, 10), set) ; if nops(adigs intersect bdigs) > 0 then true ; else false ; fi ; end: A131220 := proc(n) option remember ; local a, aprev; if n = 1 then 4 ; else aprev := A131220(n-1) ; a := aprev+1 ; while not isA001358(a) or sharedDgs(a, aprev) do a := a+1 ; od; a ; fi ; end: seq(A131220(n), n=1..40) ; # R. J. Mathar, Oct 30 2007
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Oct 20 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 30 2007
STATUS
approved