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.

%I A332265 #41 Sep 28 2020 21:47:43
%S A332265 20,3202,2056675,3500185228
%N 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.
%C A332265 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.
%e A332265 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.
%e A332265 a(1) = 3202. The smallest prime created using integers 0..7 is 1234657 while the largest is 76540231.
%e A332265 a(2) = 2056675. The smallest prime created using integers 0..10 is 10123457689 while the largest is 987654310021.
%t A332265 Table[Count[FromDigits /@  Flatten /@ IntegerDigits /@ Permutations[Range[0, 3 n + 4]], _?PrimeQ], {n, 0, 2}] (* _Robert Price_, Sep 16 2020 *)
%t A332265 (* OR, if the above runs low on memory to store all the Permutations at once... *)
%t A332265 Table[p0 = Range[0, 3n+4]; p = NextPermutation[p0]; c = 0;
%t A332265  While[p != p0,
%t A332265   If[PrimeQ[FromDigits[Flatten[IntegerDigits /@ p]]], c++];
%t A332265 p = NextPermutation[p]]; c, {n, 0, 2}] (* _Robert Price_, Sep 16 2020 *)
%Y A332265 Cf. A000040, A295206, A006879, A050288, A088628, A185122, A176009, A099182.
%K A332265 nonn,base,more
%O A332265 0,1
%A A332265 _Scott R. Shannon_, May 04 2020
%E A332265 a(3) from _Giovanni Resta_, May 04 2020