A360979 - OEIS

%I #15 Mar 04 2023 02:06:41

%S 11,13,17,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,

%T 107,113,131,151,211,223,227,229,233,239,241,251,257,263,269,277,293,

%U 311,313,331,349,353,359,383,389,401,409,421,431,433,439,443,449,457,479,487,499,503,509,521,523

%N Primes that share no digits with their digit sum.

%H Robert Israel, <a href="/A360979/b360979.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) local L,s;

%p   L:= convert(n,base,10);

%p   s:= convert(L,`+`);

%p   convert(convert(s,base,10),set) intersect convert(L,set) = {}

%p end proc:

%p select(filter, [seq(ithprime(i),i=1..1000)]);

%t Select[Prime[Range[99]],!IntersectingQ[IntegerDigits[#],List[Total[IntegerDigits[#]]]]&] (* _Stefano Spezia_, Feb 28 2023 *)

%o (PARI) isok(p) = isprime(p) && !#setintersect(Set(digits(sumdigits(p))), Set(digits(p))); \\ _Michel Marcus_, Feb 27 2023

%Y Primes not in A158473.

%Y Cf. A007605, A007953.

%K nonn,base

%O 1,1

%A _Robert Israel_, Feb 27 2023