A360986 - OEIS

%I #27 Mar 06 2023 02:59:40

%S 2,3,5,7,199,919,991,2999,9929,11177,11717,17117,31333,33331,71171,

%T 71711,161611,616111,999499,1111333,1131133,1131331,1133131,1313311,

%U 3111313,3111331,3131113,3131311,3133111,3311131,3337777,3377377,3773377,3773773,7377373,7733377,7737337,7737733,32333333

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

%H Robert Israel, <a href="/A360986/b360986.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%p dmax:= 7: # for terms with up to dmax digits

%p dsets:= proc(s, S) option remember;

%p # nondecreasing lists [x_1, ..., x_n] with sum s and set of elements S

%p    local i, x1;

%p    if S = {} then if s = 0 then return {[]} else return {} fi fi;

%p    x1:= min(S);

%p    `union`(seq(map(t -> [x1$i, op(t)], procname(s-i*x1, S minus {x1})), i=1..`if`(x1=0,dmax,floor(s/x1))))

%p end proc:

%p R:= {2,3,5,7}: count:= 4:

%p for s from 2 to 9*dmax-1 do

%p   if s mod 3 = 0 then next fi;

%p   ds:= convert(convert(s,base,10),set);

%p   DS:= select (t -> nops(t) > 1 and nops(t) <= dmax, dsets(s,ds));

%p   for r in DS do

%p      for v in remove(t -> member(t[1],[0,2,4,5,6,8]) or t[-1]=0,combinat:-permute(r)) do

%p        p:= add(v[i]*10^(i-1),i=1..nops(v));

%p        if isprime(p) then R:= R union {p}; count:= count+1;

%p       fi

%p od od od:

%p sort(convert(R,list));

%o (PARI) isok(p) = if (isprime(p), my(d=digits(p)); Set(d) == Set(digits(vecsum(d)))); \\ _Michel Marcus_, Feb 28 2023

%Y Cf. A000040, A158473.

%Y Primes in A249515.

%K nonn,base

%O 1,1

%A _Robert Israel_, Feb 27 2023