A262300 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.

2, 3, 7, 9, 11, 7, 11, 1873, 19, 14513, 13, 961

Offset: 1

Author

N. J. A. Sloane and Jerrold B. Tunnell, Sep 27 2015

Keywords

• nonn
• more
• base

Comments

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.

It is easy to check that a(19)=29.

So the sequence begins 2, 3, 7, 9, 11, 7, 11, 1873, 19, 14513, 13, 961, ???, 653, ???, 5109, 493, 757, 29, 1313, ...

a(13) is either -1 or greater than 40000. - Robert Price, Nov 03 2018

Examples

			a(5) = 11 because the smallest prime in S(5,*) (A262575) is 123467891011.
a(8) = 1873 (corresponding to the 6364-digit probable prime 1234567910111213...1873) was found by David Broadhurst on Sep 27 2015.
a(9) = 19 because the smallest prime in S(9,*) is 1234567810111213141516171819.
a(10) = 14513 (corresponding to the 61457-digit probable prime 123456789111213...14513) was found by David Broadhurst on Sep 28 2015.
		

Crossrefs

Cf. A262299.

See A262571-A262582 for the sequences S(1,*) through S(12,*).

See also A007908 (which plays the role of S(0,*)).

For the primes in S(1,*) and S(2,*) see A089987, A262298.

Programs

Mathematica

A262300[n_] := Module[{k = 1}, While[! PrimeQ[FromDigits[Flatten[Map[IntegerDigits, Complement[Range[k], {n}]]]]], k++]; k];
Table[A262300[n], {n, 12}]  (* Robert Price, Oct 27 2018 *)

PARI

s(n, k) = my(s=""); for(x=1, k, if(x!=n, s=concat(s, x))); eval(Str(s))
a(n) = for(k=1, oo, my(s=s(n, k)); if(ispseudoprime(s), return(k))) \\ Felix Fröhlich, Oct 27 2018

Extensions

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).