A065083 The least k such that precisely n near-repunit primes can be formed from (10^k-1)/9 by changing one digit from 1 to 0.

1, 3, 8, 24, 20, 12, 488, 42, 162, 4848, 642, 1682

Offset

0,2

Comments

Least inverse of A034093. - Charles R Greathouse IV, May 01 2012

a(10) = 642 and a(11) = 1682. - Charles R Greathouse IV, May 03 2012

a(>11) > 5000. - Robert Price, Nov 06 2023

Links

Table of n, a(n) for n=0..11.

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

Chris Caldwell, Repunits

Example

a(5) = 12 because R_12 = (10^12 -1)/9 = 111111111111 and from this number, by changing just one digit from 1 to 0, out of the eleven candidates, 111111111101, 111111110111, 111111011111, 111011111111 and 101111111111 are primes.

Mathematica

a = Table[0, {10} ]; Do[p = IntegerDigits[ (10^n - 1)/9]; c = 0; Do[ If[ q = FromDigits[ ReplacePart[p, 0, i]]; PrimeQ[q], c++ ], {i, 2, n} ]; If[ a[[c + 1]] == 0, a[[c + 1]] = n], {n, 1, 400} ]; a

Prog

(PARI) a(n)=my(k=1); while(sum(i=1, k-2, ispseudoprime(10^k\9-10^i)) != n, k++); k \\ Charles R Greathouse IV, May 01 2012

Crossrefs

Cf. A034093, A002275, A065074.

Sequence in context: A327151 A317362 A309114 * A280190 A037450 A081990

Adjacent sequences: A065080 A065081 A065082 * A065084 A065085 A065086

Keyword

more,nonn,base

Author

Robert G. Wilson v, Nov 19 2001

Extensions

a(6) from Charles R Greathouse IV, May 01 2012

a(9) from Robert Price, Nov 04 2023

a(10)-a(11) from comments and verified by Robert Price, Nov 04 2023

Status

approved