A360979 Primes that share no digits with their digit sum.

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

Author

Robert Israel, Feb 27 2023

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Primes not in A158473.

Cf. A007605, A007953.

Programs

Maple

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)]);

Mathematica

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

PARI

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