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%I #59 Apr 16 2024 13:36:27
%S 2,29,13,37,107,127,113,167,1033,179,137,1063,1217,1013,1399,1249,
%T 1163,1123,1307,1193,1097,10477,11351,1439,1279,1237,3947,11353,1367,
%U 10343,1973,10271,10079,10831,10321,10243,10253,10247,13093,10267,10163,10429,12487,11437,10357,10337
%N Least prime p such that exactly n distinct primes can be formed using one or more of the digits of p.
%C Inspired by A076449.
%C 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.
%C 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, ..., .
%C 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, ..., .
%C a(n) <> A076449(n) and they do not have identical digits at n = 2, 9, 15, 16, 22, 23, 28, 30, ..., .
%H David A. Corneth, <a href="/A370322/b370322.txt">Table of n, a(n) for n = 1..10000</a> (first 1755 terms from Robert G. Wilson v)
%e a(0) would be 1, but 1 is not a prime (A075053);
%e a(1) is 2, the first prime;
%e a(2) is 29 since {2 & 29} are primes but {9 & 92} are not;
%e a(3) is 13 since {3, 13 & 31} are primes, but 1 is not;
%e a(4) is 37 since all the permutations are prime, i.e.: {3, 7, 37 & 73};
%e a(5) is 107 since {7, 17, 71, 107 & 701} are primes; etc.
%t 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
%Y Cf. A072857, A075053, A076449.
%K nonn,base
%O 1,1
%A _Robert G. Wilson v_, Mar 22 2024
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