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

1,1

Comments

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..108 (all terms with <= 52 digits)

David A. Corneth, PARI program

Example

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.

Prog

(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

Crossrefs

Cf. A028864, A039986.

Sequence in context: A305835 A019384 A088987 * A217281 A322960 A348935

Adjacent sequences: A364455 A364456 A364457 * A364459 A364460 A364461

Keyword

nonn,base

Author

Jean-Marc Rebert, Dec 23 2023

Status

approved