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

5,1

Links

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

Example

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.

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

Prog

(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

Crossrefs

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

Sequence in context: A281301 A286481 A168334 * A095434 A276377 A183085

Adjacent sequences: A358017 A358018 A358019 * A358021 A358022 A358023

Keyword

nonn,base

Author

Jean-Marc Rebert, Oct 24 2022

Status

approved