A360986 Primes whose sum of decimal digits has the same set of decimal digits as the prime.

2, 3, 5, 7, 199, 919, 991, 2999, 9929, 11177, 11717, 17117, 31333, 33331, 71171, 71711, 161611, 616111, 999499, 1111333, 1131133, 1131331, 1133131, 1313311, 3111313, 3111331, 3131113, 3131311, 3133111, 3311131, 3337777, 3377377, 3773377, 3773773, 7377373, 7733377, 7737337, 7737733, 32333333

Offset: 1

Author

Robert Israel, Feb 27 2023

Keywords

• nonn
• base

Examples

			a(5) = 199 is a term because 199 is prime and 1+9+9 = 19 has the same set {1,9} of decimal digits as 199.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A158473.

Primes in A249515.

Programs

Maple

dmax:= 7: # for terms with up to dmax digits
dsets:= proc(s, S) option remember;
# nondecreasing lists [x_1, ..., x_n] with sum s and set of elements S
   local i, x1;
   if S = {} then if s = 0 then return {[]} else return {} fi fi;
   x1:= min(S);
   `union`(seq(map(t -> [x1$i, op(t)], procname(s-i*x1, S minus {x1})), i=1..`if`(x1=0,dmax,floor(s/x1))))
end proc:
R:= {2,3,5,7}: count:= 4:
for s from 2 to 9*dmax-1 do
  if s mod 3 = 0 then next fi;
  ds:= convert(convert(s,base,10),set);
  DS:= select (t -> nops(t) > 1 and nops(t) <= dmax, dsets(s,ds));
  for r in DS do
     for v in remove(t -> member(t[1],[0,2,4,5,6,8]) or t[-1]=0,combinat:-permute(r)) do
       p:= add(v[i]*10^(i-1),i=1..nops(v));
       if isprime(p) then R:= R union {p}; count:= count+1;
      fi
od od od:
sort(convert(R,list));

PARI

isok(p) = if (isprime(p), my(d=digits(p)); Set(d) == Set(digits(vecsum(d)))); \\ Michel Marcus, Feb 28 2023