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%I #66 Nov 04 2018 20:29:08
%S 2,3,7,9,11,7,11,1873,19,14513,13,961
%N Let S(n,k) denote the number formed by concatenating the decimal numbers 1,2,3,...,k, but omitting n; a(n) is the smallest k for which S(n,k) is prime, or -1 if no term in S(n,*) is prime.
%C Sep 28 2015: _David Broadhurst_ has found a(10) = 14513, a(12) = 961, a(14) = 653, a(16) = 5109, a(17) = 493, a(18) = 757, and a(20) = 1313. All these correspond to probable primes.
%C It is easy to check that a(19)=29.
%C So the sequence begins 2, 3, 7, 9, 11, 7, 11, 1873, 19, 14513, 13, 961, ???, 653, ???, 5109, 493, 757, 29, 1313, ...
%C a(13) is either -1 or greater than 40000. - _Robert Price_, Nov 03 2018
%e a(5) = 11 because the smallest prime in S(5,*) (A262575) is 123467891011.
%e a(8) = 1873 (corresponding to the 6364-digit probable prime 1234567910111213...1873) was found by David Broadhurst on Sep 27 2015.
%e a(9) = 19 because the smallest prime in S(9,*) is 1234567810111213141516171819.
%e a(10) = 14513 (corresponding to the 61457-digit probable prime 123456789111213...14513) was found by David Broadhurst on Sep 28 2015.
%t A262300[n_] := Module[{k = 1}, While[! PrimeQ[FromDigits[Flatten[Map[IntegerDigits, Complement[Range[k], {n}]]]]], k++]; k];
%t Table[A262300[n], {n, 12}] (* _Robert Price_, Oct 27 2018 *)
%o (PARI) s(n, k) = my(s=""); for(x=1, k, if(x!=n, s=concat(s, x))); eval(Str(s))
%o a(n) = for(k=1, oo, my(s=s(n, k)); if(ispseudoprime(s), return(k))) \\ _Felix Fröhlich_, Oct 27 2018
%Y Cf. A262299.
%Y See A262571-A262582 for the sequences S(1,*) through S(12,*).
%Y See also A007908 (which plays the role of S(0,*)).
%Y For the primes in S(1,*) and S(2,*) see A089987, A262298.
%K nonn,more,base
%O 1,1
%A _N. J. A. Sloane_ and Jerrold B. Tunnell, Sep 27 2015
%E a(8) was found by _David Broadhurst_, Sep 27 2015. On Sep 28 2015 _David Broadhurst_ also found a(10), a(12), a(14), a(16), a(17), a(18), and a(20).
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