A332265 a(n) is the number of prime numbers created when concatenating all the arrangements of the decimal integers from 0 to 3*n+4.

20, 3202, 2056675, 3500185228

Offset

0,1

Comments

Only 4 and every third integer after 4 can create primes when concatenating the integer arrangements of 0,...,3*n+4 as the other integer values will create numbers with digit sums divisible by 3, and hence are divisible by 3. The digit 0 is allowed to be the first digit in the number but is then ignored when determining if the remaining digits form a prime.

Links

Table of n, a(n) for n=0..3.

Example

a(0) = 20 as there are twenty primes created when concatenating the integer arrangements of 0,1,2,3,4. They are 1423, 2143, 2341, 4231, 10243, 12043, 20143, 20341, 20431, 23041, 24103, 30241, 32401, 40123, 40213, 40231, 41023, 41203, 42013, 43201.
a(1) = 3202. The smallest prime created using integers 0..7 is 1234657 while the largest is 76540231.
a(2) = 2056675. The smallest prime created using integers 0..10 is 10123457689 while the largest is 987654310021.

Mathematica

Table[Count[FromDigits /@  Flatten /@ IntegerDigits /@ Permutations[Range[0, 3 n + 4]], _?PrimeQ], {n, 0, 2}] (* Robert Price, Sep 16 2020 *)
(* OR, if the above runs low on memory to store all the Permutations at once... *)
Table[p0 = Range[0, 3n+4]; p = NextPermutation[p0]; c = 0;
 While[p != p0,
  If[PrimeQ[FromDigits[Flatten[IntegerDigits /@ p]]], c++];
p = NextPermutation[p]]; c, {n, 0, 2}] (* Robert Price, Sep 16 2020 *)

Crossrefs

Cf. A000040, A295206, A006879, A050288, A088628, A185122, A176009, A099182.

Sequence in context: A145405 A028458 A225989 * A177323 A184891 A279297

Adjacent sequences: A332262 A332263 A332264 * A332266 A332267 A332268

Keyword

nonn,base,more

Author

Scott R. Shannon, May 04 2020

Extensions

a(3) from Giovanni Resta, May 04 2020

Status

approved