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

1,1

Links

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

Example

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.

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));

Prog

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

Crossrefs

Cf. A000040, A158473.

Primes in A249515.

Sequence in context: A046478 A046475 A029978 * A122764 A256886 A195302

Adjacent sequences: A360983 A360984 A360985 * A360987 A360988 A360989

Keyword

nonn,base

Author

Robert Israel, Feb 27 2023

Status

approved