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

1,1

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

Links

Table of n, a(n) for n=1..12.

Example

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.

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 *)

Prog

(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

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.

Sequence in context: A152863 A047359 A027700 * A202105 A076297 A174184

Adjacent sequences: A262297 A262298 A262299 * A262301 A262302 A262303

Keyword

nonn,more,base

Author

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

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).

Status

approved