|
%I #31 Sep 14 2022 20:28:01
%S 4,6,9,22,33,55,77,111,1111,11111,1111111,11111111111,
%T 11111111111111111,2222222222222222222,3333333333333333333,
%U 5555555555555555555,7777777777777777777,22222222222222222222222,33333333333333333333333,55555555555555555555555
%N Repdigit semiprimes (semiprimes composed of identical digits).
%C A semiprime can be repdigit (base 10) in only three ways. It can be a single-digit semiprime, a repunit semiprime (A102782), or a repunit prime times a prime digit {2, 3, 5, 7}. Occurs in proof that the sequence is infinite in which a(n) is the least semiprime > a(n-1) such that a(n) has no digit in common with a(n-1). - _Jonathan Vos Post_; corrected by _Max Alekseyev_, Sep 14 2022
%H Max Alekseyev, <a href="/A196104/b196104.txt">Table of n, a(n) for n = 1..35</a>
%F Union of {4, 6, 9}, A102782, 2*A004022, 3*A004022, 5*A004022, and 7*A004022. - _Jonathan Vos Post_ and _R. J. Mathar_, Oct 27 2011
%e a(12) = 11111111111 = 21649 * 513239 is semiprime.
%p with(numtheory):for n from 1 to 23 do:for b from 1 to 9 do:x:=(((10^n)- 1)/9)*b:if bigomega(x)=2 then printf(`%d, `,x):else fi:od:od:
%t Select[FromDigits/@Flatten[Table[PadRight[{},i,n],{i,25},{n,9}],1], PrimeOmega[ #] ==2&] (* _Harvey P. Dale_, Mar 11 2019 *)
%o (PARI) print1("4, 6, 9");for(n=1,20,t=10^n\9;if(bigomega(t)==2,print1(", "t)); if(isprime(t),forprime(p=2,7,print1(", "p*t)))) \\ _Charles R Greathouse IV_, Oct 27 2011
%Y Subsequence of A046328.
%Y Except for initial terms, subsequence of A116063.
%Y Cf. A000042, A001358, A004023, A046413, A102782.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Oct 27 2011
%E Edited by _Max Alekseyev_, Sep 14 2022
|
