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A158473 Primes whose digit sum contains one or more digits of the same prime.

%I A158473 #17 Apr 03 2023 10:36:11
%S A158473 2,3,5,7,19,109,127,137,139,149,157,163,167,173,179,181,191,193,197,
%T A158473 199,271,281,283,307,317,337,347,367,373,379,397,419,461,463,467,491,
%U A158473 541,557,571,613,617,619,631,641,643,647,661,673,691,719,733,739,743,751
%N A158473 Primes whose digit sum contains one or more digits of the same prime.
%H A158473 Robert Israel, <a href="/A158473/b158473.txt">Table of n, a(n) for n = 1..10000</a>
%H A158473 Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The First 1,000 Primes</a>
%e A158473 139 is a prime whose digit sum of 13 contains the digits 1 and 3 which are also in the prime.
%e A158473 149 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.
%e A158473 419 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.
%p A158473 filter:= proc(n) local L,s;
%p A158473   L:= convert(n,base,10);
%p A158473   s:= convert(L,`+`);
%p A158473   convert(convert(s,base,10),set) intersect convert(L,set) <> {}
%p A158473 end proc:
%p A158473 select(filter, [seq(ithprime(i),i=1..100)]); # _Robert Israel_, Feb 27 2023
%o A158473 (PARI) isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(sumdigits(p)))) >= 1); \\ _Michel Marcus_, Nov 12 2017
%Y A158473 Cf. A107579, A158217, A158293.
%K A158473 base,nonn
%O A158473 1,1
%A A158473 _Parthasarathy Nambi_, Mar 20 2009
%E A158473 Single-digit primes added by _R. J. Mathar_, Jul 08 2009
%E A158473 Typos in data corrected by _D. S. McNeil_ and _Andrew Weimholt_, Aug 17 2010