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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.

%I A358020 #22 Oct 25 2022 20:05:21
%S A358020 1111111111111111111,31,71,191,223,229,113,73,4111,433,4447,353,599,
%T A358020 661,677,1117,337,97,383,8999,797,10111,1013,701,1009,131,271,311,173,
%U A358020 193,419,1151,571,613,617,317,197,811,199,1193,719,911,2111,233,277,929,2333,293,421,521,2557
%N 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.
%H A358020 Jean-Marc Rebert, <a href="/A358020/b358020.txt">Table of n, a(n) for n = 5..10000</a>
%e A358020 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.
%e A358020 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.
%e A358020 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.
%p A358020 N:= 60: # for a(5)..a(N)
%p A358020 A:= Array(5..N):
%p A358020 R:= 1111111111111111111:
%p A358020 A[5]:= R: count:= 1:
%p A358020 for k from 6 while count < N-4 do
%p A358020   p:= ithprime(k);
%p A358020   S:= convert(convert(p,base,10),set);
%p A358020   if assigned(V[S]) and V[S]<=N then A[V[S]]:= p; count:=count+1;  fi;
%p A358020   V[S]:= k;
%p A358020 od:
%p A358020 convert(A,list); # _Robert Israel_, Oct 25 2022
%o A358020 (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)))
%o A358020 (Python)
%o A358020 from sympy import isprime, prime
%o A358020 from itertools import count, product
%o A358020 def a(n):
%o A358020     pn = prime(n)
%o A358020     s = str(pn)
%o A358020     for d in count(len(s)):
%o A358020         for p in product(set(s), repeat=d):
%o A358020             if p[0] == "0": continue
%o A358020             t = int("".join(p))
%o A358020             if t > pn and isprime(t):
%o A358020                 return t
%o A358020 print([a(n) for n in range(5, 56)]) # _Michael S. Branicky_, Oct 25 2022
%Y A358020 Cf. A000040, A357096, A004022, A004023, A020451, A020455, A050288, A166681.
%K A358020 nonn,base
%O A358020 5,1
%A A358020 _Jean-Marc Rebert_, Oct 24 2022