A176009 -id:A176009 - cp's OEIS frontend

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

Scott R. Shannon, May 04 2020

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.

			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.

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

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 *)

a(3) from Giovanni Resta, May 04 2020

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions