A034093 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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