A196104 Repdigit semiprimes (semiprimes composed of identical digits).

4, 6, 9, 22, 33, 55, 77, 111, 1111, 11111, 1111111, 11111111111, 11111111111111111, 2222222222222222222, 3333333333333333333, 5555555555555555555, 7777777777777777777, 22222222222222222222222, 33333333333333333333333, 55555555555555555555555

Offset: 1

Author

Michel Lagneau, Oct 27 2011

Keywords

• nonn
• base

Comments

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

Examples

			a(12) = 11111111111 = 21649 * 513239 is semiprime.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..35

Crossrefs

Subsequence of A046328.

Except for initial terms, subsequence of A116063.

Cf. A000042, A001358, A004023, A046413, A102782.

Programs

Maple

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:

Mathematica

Select[FromDigits/@Flatten[Table[PadRight[{},i,n],{i,25},{n,9}],1], PrimeOmega[ #] ==2&] (* Harvey P. Dale, Mar 11 2019 *)

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

Formula

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

Extensions

Edited by Max Alekseyev, Sep 14 2022