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.

19, 23, 29, 47, 59, 67, 89, 223, 227, 229, 233, 257, 269, 449, 499, 557, 599, 677, 1447, 2267, 2447, 4447, 5557, 8999, 11119, 15559, 22229, 22669, 23333, 24889, 44449, 48889, 55589, 55889, 59999, 79999, 222269, 444449, 455557, 555557, 555589, 666667, 4444469, 4555559

Offset: 1

Author

Jean-Marc Rebert, Dec 23 2023

Keywords

• nonn
• base

Comments

The least terms with respectively 2, 3, 4 distinct digits are 19, 257, 24889.

Examples

			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.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..108 (all terms with <= 52 digits)
• David A. Corneth, PARI program

Crossrefs

Cf. A028864, A039986.

Programs

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

PARI

\\ See PARI link

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations as mp
from itertools import count, islice, combinations_with_replacement as mc
def bgen(d): yield from ("".join(m) for m in mc("123456789", d))
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)))
print(list(islice(agen(), 44))) # Michael S. Branicky, Dec 23 2023