A158473 - OEIS

%I #17 Apr 03 2023 10:36:11

%S 2,3,5,7,19,109,127,137,139,149,157,163,167,173,179,181,191,193,197,

%T 199,271,281,283,307,317,337,347,367,373,379,397,419,461,463,467,491,

%U 541,557,571,613,617,619,631,641,643,647,661,673,691,719,733,739,743,751

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

%H Robert Israel, <a href="/A158473/b158473.txt">Table of n, a(n) for n = 1..10000</a>

%H Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The First 1,000 Primes</a>

%e 139 is a prime whose digit sum of 13 contains the digits 1 and 3 which are also in the prime.

%e 149 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.

%e 419 is a prime whose digit sum of 14 contains the digits 1 and 4 which are also in the prime.

%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..100)]); # _Robert Israel_, Feb 27 2023

%o (PARI) isok(p) = isprime(p) && (#setintersect(Set(digits(p)), Set(digits(sumdigits(p)))) >= 1); \\ _Michel Marcus_, Nov 12 2017

%Y Cf. A107579, A158217, A158293.

%K base,nonn

%O 1,1

%A _Parthasarathy Nambi_, Mar 20 2009

%E Single-digit primes added by _R. J. Mathar_, Jul 08 2009

%E Typos in data corrected by _D. S. McNeil_ and _Andrew Weimholt_, Aug 17 2010