A262575 -id:A262575 - cp's OEIS frontend

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

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

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

			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.

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.

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 *)

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

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).

A262552 Numbers n such that the concatenation of the decimal numbers 1 through n, but omitting 5, is a prime.

Original entry on oeis.org

11, 17, 157, 3631

Offset: 1

N. J. A. Sloane, Oct 09 2015

The corresponding primes are the primes in A262575.
The actual values of a(1) to a(4) are also primes, although that is not a necessary condition for a number to belong to this sequence. Not all the terms of A262300 are primes, for example.
Probabilistic arguments suggest the sequence is infinite.
a(5) > 10000. - Robert Price, Nov 03 2018

			The first two terms correspond to the primes 123467891011 and 123467891011121314151617.
a(3) corresponds to a 362-digit prime, a(4) to a 13416-digit probable prime. These two terms were found by _David Broadhurst_ on Oct 08 2015.

Cf. A262575, A262300, A007908.

cp's OEIS Frontend

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.

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