A358020 Least prime number > prime(n) (n >= 5) whose set of decimal digits coincides with the set of decimal digits of prime(n), or -1 if no such prime exists.

1111111111111111111, 31, 71, 191, 223, 229, 113, 73, 4111, 433, 4447, 353, 599, 661, 677, 1117, 337, 97, 383, 8999, 797, 10111, 1013, 701, 1009, 131, 271, 311, 173, 193, 419, 1151, 571, 613, 617, 317, 197, 811, 199, 1193, 719, 911, 2111, 233, 277, 929, 2333, 293, 421, 521, 2557

Offset: 5

Author

Jean-Marc Rebert, Oct 24 2022

Keywords

• nonn
• base

Examples

			prime(6) = 13 and the prime number 31 have the same set of digits {1,3}, and 31 is the smallest such number, hence a(6) = 31.
prime(13) = 41 and the prime number 4111 have the same set of digits {1,4}, and 4111 is the smallest such number, hence a(13) = 4111.
prime(20) = 71 and the prime number 1117 have the same set of digits {1,7}, and 1117 is the smallest such number, hence a(20) = 1117.
		

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 5..10000

Crossrefs

Cf. A000040, A357096, A004022, A004023, A020451, A020455, A050288, A166681.

Programs

Maple

N:= 60: # for a(5)..a(N)
A:= Array(5..N):
R:= 1111111111111111111:
A[5]:= R: count:= 1:
for k from 6 while count < N-4 do
  p:= ithprime(k);
  S:= convert(convert(p,base,10),set);
  if assigned(V[S]) and V[S]<=N then A[V[S]]:= p; count:=count+1;  fi;
  V[S]:= k;
od:
convert(A,list); # Robert Israel, Oct 25 2022

PARI

a(n)=my(m=Set(digits(prime(n)))); if(n<5, return()); if(n==5,return(1111111111111111111));forprime(p=prime(n+1), , if(Set(digits(p))==m, return(p)))

Python

from sympy import isprime, prime
from itertools import count, product
def a(n):
    pn = prime(n)
    s = str(pn)
    for d in count(len(s)):
        for p in product(set(s), repeat=d):
            if p[0] == "0": continue
            t = int("".join(p))
            if t > pn and isprime(t):
                return t
print([a(n) for n in range(5, 56)]) # Michael S. Branicky, Oct 25 2022