A003021 -id:A003021 - cp's OEIS frontend

A269503 Largest prime factor of A138148(n).

101, 13, 137, 9091, 9901, 909091, 5882353, 52579, 333667, 9091, 99990001, 1058313049, 265371653, 909091, 2906161, 21993833369, 999999000001, 909090909090909091, 1111111111111111111, 909091, 1056689261, 549797184491917, 11111111111111111111111

Offset: 1

Altug Alkan, May 11 2016

nonn

Largest prime factor of (10^(n+1)+1)*(10^n-1)/9.

			a(4) = 9091 because largest prime factor of 111101111 is 9091.

Max Alekseyev, Table of n, a(n) for n = 1..344

Cf. A003020, A003021, A006530, A138148.

seq(max(max(numtheory:-factorset((10^n-1)/9)),
max(numtheory:-factorset(10^(n+1)+1))), n=1..30); # Robert Israel, May 11 2016

a006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
for(n=1, 25, print1(a006530((10^(2*n+1)-1)/9-10^n), ", "));

a(n) = max(A003020(n),A003021(n+1)) for n >= 2. - Robert Israel, May 11 2016

A309358 Numbers k such that 10^k + 1 is a semiprime.

Original entry on oeis.org

4, 5, 6, 7, 8, 19, 31, 53, 67, 293, 586, 641, 922, 2137, 3011

Offset: 1

Hugo Pfoertner, Jul 29 2019

a(16) > 12000.
10^k + 1 is composite unless k is a power of 2, and it can be conjectured that it is composite for all k > 2, cf. A038371 and A185121. - M. F. Hasler, Jul 30 2019
Suppose k is odd. Then k is a term if and only if (10^k+1)/11 is prime. - Chai Wah Wu, Jul 31 2019

			a(1) = 4 because 10^4 + 1 = 10001 = 73*137.

Cf. A003021, A038371, A046413, A057934, A062397, A092559.

Odd terms in sequence: A001562.

IsSemiprime:=func; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // Vincenzo Librandi, Jul 31 2019

Mathematica

Select[Range[200], Plus@@Last/@FactorInteger[10^# + 1] == 2 &] (* Vincenzo Librandi, Jul 31 2019 *)

cp's OEIS Frontend

A269503 Largest prime factor of A138148(n).

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