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A364458 Prime numbers that are not repdigits with digits in nondecreasing order with the property that any nontrivial permutation of the digits gives a composite number.

%I A364458 #118 Jan 03 2024 09:49:27
%S A364458 19,23,29,47,59,67,89,223,227,229,233,257,269,449,499,557,599,677,
%T A364458 1447,2267,2447,4447,5557,8999,11119,15559,22229,22669,23333,24889,
%U A364458 44449,48889,55589,55889,59999,79999,222269,444449,455557,555557,555589,666667,4444469,4555559
%N A364458 Prime numbers that are not repdigits with digits in nondecreasing order with the property that any nontrivial permutation of the digits gives a composite number.
%C A364458 The least terms with respectively 2, 3, 4 distinct digits are 19, 257, 24889.
%H A364458 Michael S. Branicky, <a href="/A364458/b364458.txt">Table of n, a(n) for n = 1..108</a> (all terms with <= 52 digits)
%H A364458 David A. Corneth, <a href="/A364458/a364458.gp.txt">PARI program</a>
%e A364458 19 is a term, because the digits of 19 are in nondecreasing order and 91 is the unique number != 19 given by a permutation of 19 and 91 = 7 * 13 is composite and the digits of 91 are not in nondecreasing order.
%o A364458 (PARI) is(k)=my(u=digits(k),n=#u);if(#vecsort(u,,8)==1||u!=vecsort(u)||!isprime(k),return(0));forperm(n,p,my(vp=Vec(p),v=[]);for(i=1,n,v=concat(v,u[vp[i]]));q=fromdigits(v);if(k!=q&&isprime(q),return(0)));1
%o A364458 (PARI) \\ See PARI link
%o A364458 (Python)
%o A364458 from sympy import isprime
%o A364458 from sympy.utilities.iterables import multiset_permutations as mp
%o A364458 from itertools import count, islice, combinations_with_replacement as mc
%o A364458 def bgen(d): yield from ("".join(m) for m in mc("123456789", d))
%o A364458 def agen(): yield from (t for d in count(1) for k in bgen(d) if len(set(k))!=1 and isprime(t:=int(k)) if not any((j:="".join(m))!=k and isprime(int(j)) for m in mp(k)))
%o A364458 print(list(islice(agen(), 44))) # _Michael S. Branicky_, Dec 23 2023
%Y A364458 Cf. A028864, A039986.
%K A364458 nonn,base
%O A364458 1,1
%A A364458 _Jean-Marc Rebert_, Dec 23 2023