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%I #23 Nov 06 2023 14:10:09
%S 1,3,8,24,20,12,488,42,162,4848,642,1682
%N 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.
%C Least inverse of A034093. - _Charles R Greathouse IV_, May 01 2012
%C a(10) = 642 and a(11) = 1682. - _Charles R Greathouse IV_, May 03 2012
%C a(>11) > 5000. - _Robert Price_, Nov 06 2023
%H Chris Caldwell, <a href="https://t5k.org/curios/page.php?number_id=169">Below are all of the 12-digit Near-Repunit primes:</a>
%H Chris Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Repunit">Repunits</a>
%e 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.
%t 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
%o (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
%Y Cf. A034093, A002275, A065074.
%K more,nonn,base
%O 0,2
%A _Robert G. Wilson v_, Nov 19 2001
%E a(6) from _Charles R Greathouse IV_, May 01 2012
%E a(9) from _Robert Price_, Nov 04 2023
%E a(10)-a(11) from comments and verified by _Robert Price_, Nov 04 2023
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