A153328 Numbers k such that (10^k-1)*120/99 + 1 is prime.

6, 10, 42, 138, 626, 1398, 1596, 1978, 7808, 14058, 46498

Offset: 1

Author

Cino Hilliard, Dec 23 2008

Keywords

• nonn
• base
• more

Comments

Also 2*A056803 which I took the liberty of using to create the last 2 entries.

These numbers are always even. If n is odd, then 10^n-1 produces a number with an odd number of 9's which 99 does not divide. a(6), a(10), a(42) are 1212121, 12121212121, 1212121212121212121212121212121212121212121 which can be found in A092696. Also, the formula produce palindromic numbers.

Crossrefs

Cf. A092696, A056803.

Programs

PARI

/* n=number of values to test; r=repeat digits, e.g., 12, 121, 177, 1234; d = last digit appended to the end */
repr(n,r,d) = ln=length(Str(r));for(x=0,n,y=(10^(ln*x)-1)*10*r/ (10^ln-1)+1;if(ispseudoprime(y),print1(ln*x",")))

Extensions

a(11) from Michael S. Branicky, Dec 11 2024