A370322 Least prime p such that exactly n distinct primes can be formed using one or more of the digits of p.

2, 29, 13, 37, 107, 127, 113, 167, 1033, 179, 137, 1063, 1217, 1013, 1399, 1249, 1163, 1123, 1307, 1193, 1097, 10477, 11351, 1439, 1279, 1237, 3947, 11353, 1367, 10343, 1973, 10271, 10079, 10831, 10321, 10243, 10253, 10247, 13093, 10267, 10163, 10429, 12487, 11437, 10357, 10337

Offset: 1

Author

Robert G. Wilson v, Mar 22 2024

Keywords

• nonn
• base

Comments

Inspired by A076449.

a(n) >= A076449(n). As an example, a(727) is 3569887, but A076449(727) is 3567889, a difference of 1998. Notice that they possess identical digits.

a(n) = A076449(n) at n = 1, 3, 4, 5, 6, 7, 8, 10, 11, 14, 18, 19, 25, 26, 29, 33, 38, 40, 45, 46, ..., .

a(n) <> A076449(n) but they have identical digits at n = 12, 13, 17, 19, 20, 21, 24, 27, 31, 32, 34, 35, 36, 37, 39, ..., .

a(n) <> A076449(n) and they do not have identical digits at n = 2, 9, 15, 16, 22, 23, 28, 30, ..., .

Examples

			a(0) would be 1, but 1 is not a prime (A075053);
a(1) is 2, the first prime;
a(2) is 29 since {2 & 29} are primes but {9 & 92} are not;
a(3) is 13 since {3, 13 & 31} are primes, but 1 is not;
a(4) is 37 since all the permutations are prime, i.e.: {3, 7, 37 & 73};
a(5) is 107 since {7, 17, 71, 107 & 701} are primes; etc.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1755 terms from Robert G. Wilson v)

Crossrefs

Cf. A072857, A075053, A076449.

Programs

Mathematica

f = Compile[{{n, Integer}}, Floor@ Length[ Select[ Union[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits@n], 1]], PrimeQ@# &]]]; p = 2; t[] := 0; While[p < 114500, a = f@p; If[ t[a] == 0, t[a] = p]; p = NextPrime@ p]; t /@ Range@ 100