A034093 Number of near-repunit primes that can be formed from (10^k - 1)/9 by changing just one digit from 1 to 0.

0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 0, 5, 0, 0, 0, 0, 2, 5, 0, 4, 0, 0, 0, 3, 0, 1, 0, 0, 1, 2, 0, 4, 1, 0, 1, 2, 0, 2, 1, 0, 0, 7, 0, 4, 0, 0, 0, 2, 0, 2, 1, 0, 1, 3, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 1, 3, 0, 1, 0, 0, 1, 3, 0, 3, 0, 0, 1, 1, 0, 1, 0, 0, 0, 2, 0, 3, 0, 0

Offset

1,8

References

C. K. Caldwell and H. Dubner, The near repunits primes, J. Rec. Math., Vol. 27(1), 1995, pp. 35-41.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..2000

Chris Caldwell, Below are all of the 12-digit Near-Repunit primes.

Chris Caldwell, Repunits.

Example

a(12) = 5 because from (10^12 - 1)/9 = 111111111111, by changing just one digit from 1 to 0, out of the eleven candidates, 111111111101, 111111110111, 111111011111, 111011111111 and 101111111111 are primes.

Mathematica

a = {}; Do[ p = IntegerDigits[ (10^n - 1)/9 ]; c = 0; Do[ If[ q = FromDigits[ ReplacePart[p, 0, i]]; PrimeQ[q], c++ ], {i, 2, n} ]; a = Append[a, c], {n, 1, 100} ]; a (* Robert G. Wilson v, Nov 19 2001 *)

Prog

(PARI) a(n)=sum(i=1, n-2, ispseudoprime(10^n\9-10^i)) \\ Charles R Greathouse IV, May 01 2012
(Python)
from sympy import isprime
def a(n):
    Rn = (10**n-1)//9
    return sum(1 for i in range(n-1) if isprime(Rn-10**i))
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Nov 04 2023

Crossrefs

Cf. A004022, A065074, A065083.

Sequence in context: A274777 A136129 A278213 * A246187 A079508 A057150

Adjacent sequences: A034090 A034091 A034092 * A034094 A034095 A034096

Keyword

nonn,base

Author

Felice Russo

Extensions

More terms from Robert G. Wilson v, Nov 19 2001

Edited by N. J. A. Sloane, Oct 02 2008 at the suggestion of R. J. Mathar

Status

approved