A131220 a(n) is the least semiprime > a(n-1) whose digits do not appear in a(n-1).

4, 6, 9, 10, 22, 33, 46, 51, 62, 74, 82, 91, 202, 314, 502, 611, 703, 815, 922, 1003, 2227, 3005, 4117, 5006, 7111, 8002, 9111, 20003, 41119, 50003, 61111, 70027, 81113, 90026, 111113, 200006, 311113, 400006, 511113, 600007

Offset

1,1

Comments

Semiprime analog of A030284.

Links

Table of n, a(n) for n=1..40.

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

Cf. A001358, A030284.

Sequence in context: A084668 A085842 A356135 * A332618 A295329 A302990

Adjacent sequences: A131217 A131218 A131219 * A131221 A131222 A131223

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Oct 20 2007

Extensions

More terms from R. J. Mathar, Oct 30 2007

Status

approved