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

1,1

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, ..., .

Links

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

Example

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.

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

Crossrefs

Cf. A072857, A075053, A076449.

Sequence in context: A090497 A128371 A175932 * A225544 A153655 A153657

Adjacent sequences: A370319 A370320 A370321 * A370323 A370324 A370325

Keyword

nonn,base

Author

Robert G. Wilson v, Mar 22 2024

Status

approved