A158473 -id:A158473 - cp's OEIS frontend

A052019 Sum of digits of prime p is substring of p.

2, 3, 5, 7, 109, 139, 149, 179, 199, 911, 919, 1009, 1063, 1109, 1163, 1181, 1327, 1381, 1409, 1427, 1481, 1609, 1627, 1663, 1709, 1811, 2099, 2137, 2399, 2699, 2711, 2713, 2719, 2999, 3613, 3617, 4513, 4517, 4519, 5413, 5417, 5419, 6113, 6133, 6143

Offset: 1

Patrick De Geest, Nov 15 1999

Cf. A052018, A052020, A052021, A052022, A007953, A005349, A028834 & A158473.

fQ[n_] := Block[ {id = IntegerDigits@ n}, pid = Plus @@ id; MemberQ[ Partition[id, IntegerLength@ pid, 1], IntegerDigits@ pid]]; Select[ Prime@ Range@ 802, fQ] (* Robert G. Wilson v, Aug 16 2011 *)
Select[Prime[Range[1000]],SequenceCount[IntegerDigits[#], IntegerDigits[ Total[ IntegerDigits[ #]]]]> 0&] (* The program uses the SequenceCount function from Mathematica version 10 *)  (* Harvey P. Dale, Sep 30 2015 *)

A360979 Primes that share no digits with their digit sum.

Original entry on oeis.org

11, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 113, 131, 151, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 277, 293, 311, 313, 331, 349, 353, 359, 383, 389, 401, 409, 421, 431, 433, 439, 443, 449, 457, 479, 487, 499, 503, 509, 521, 523

Offset: 1

Robert Israel, Feb 27 2023

			a(5) = 29 is a term because 29 is prime and 2+9 = 11 shares no digits with 29.

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

Primes not in A158473.

Cf. A007605, A007953.

filter:= proc(n) local L,s;
  L:= convert(n,base,10);
  s:= convert(L,`+`);
  convert(convert(s,base,10),set) intersect convert(L,set) = {}
end proc:
select(filter, [seq(ithprime(i),i=1..1000)]);

Select[Prime[Range[99]],!IntersectingQ[IntegerDigits[#],List[Total[IntegerDigits[#]]]]&] (* Stefano Spezia, Feb 28 2023 *)

isok(p) = isprime(p) && !#setintersect(Set(digits(sumdigits(p))), Set(digits(p))); \\ Michel Marcus, Feb 27 2023

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

Original entry on oeis.org

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

Robert Israel, Feb 27 2023

			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.

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

Cf. A000040, A158473.

Primes in A249515.

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));

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

cp's OEIS Frontend

A052019 Sum of digits of prime p is substring of p.

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Mathematica

A360979 Primes that share no digits with their digit sum.

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Maple

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

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Programs

Maple

PARI