A179005 -id:A179005 - cp's OEIS frontend

A259102 Composite repunits with a prime number of 1's.

111, 11111, 1111111, 11111111111, 1111111111111, 11111111111111111, 11111111111111111111111111111, 1111111111111111111111111111111, 1111111111111111111111111111111111111, 11111111111111111111111111111111111111111, 1111111111111111111111111111111111111111111

Offset: 1

N. J. A. Sloane, Jun 23 2015

Alois P. Heinz, Table of n, a(n) for n = 1..164
R. Ondrejka, Letter to N. J. A. Sloane, May 15 1976

Cf. A002275, A004022, A004023, A031974, A179005.

f:=n->(10^n-1)/9; [f(3),f(5),f(7),f(11),f(13),f(17),f(29),f(31),f(37),f(41),f(43),f(47)];  # cf. A004023
# second Maple program:
r:= n-> (10^n-1)/9:
b:= proc(n) option remember; local p;
      p:=`if`(n=1, 1, b(n-1));
      do p:= nextprime(p);
         if not isprime(r(p)) then return p fi
      od
    end:
a:= n-> r(b(n)):
seq(a(n), n=1..15);  # Alois P. Heinz, Jun 25 2015

A199979 Nonprime numbers whose multiplicative digital root is 1.

Original entry on oeis.org

1, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, 111111111111111111, 11111111111111111111, 111111111111111111111

Offset: 1

Jaroslav Krizek, Nov 13 2011

1 and the composite repunits.

Number of 1's in a(n) is in A179005. Complement of A004022 with respect to A002275.

			1111 has a multiplicative digital root of 1 and it is the product of 11 and 101, therefore it is in the sequence.
11 has a multiplicative digital root of 1 but it is a prime number and therefore it is not in the sequence.

Cf. A004022 (primes whose multiplicative digital root is 1).

Select[Table[(10^n - 1)/9, {n, 20}], Not[PrimeQ[#]] &] (* Alonso del Arte, Nov 23 2011 *)

cp's OEIS Frontend

A259102 Composite repunits with a prime number of 1's.

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A199979 Nonprime numbers whose multiplicative digital root is 1.

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Mathematica