A330600 - OEIS

%I #14 Sep 08 2022 08:46:24

%S 17,23,29,37,53,67,83,97,107,113,127,131,139,157,163,167,173,181,191,

%T 193,199,223,227,233,241,251,281,283,307,311,313,331,337,353,367,379,

%U 383,397,409,421,431,433,439,457,463,467,499,503,521,523,541,569,571,587,593,613,631,643,647,659,661

%N Primes p such that the sum of (p mod d) for nonzero digits d of p is prime.

%H Robert Israel, <a href="/A330600/b330600.txt">Table of n, a(n) for n = 1..10000</a>

%e a(10) = 113 is in the sequence because 113 is prime and (113 mod 1) + (113 mod 1) + (113 mod 3) = 2 is prime.

%p filter:= proc(n) local t;

%p    isprime(n) and isprime(add(n mod t, t = subs(0=NULL, convert(n,base,10))))

%p end proc:

%p select(filter, [seq(i,i=3..1000,2)]);

%t smdQ[n_]:=PrimeQ[Total[Mod[n,Select[IntegerDigits[n],#!=0&]]]]; Select[ Prime[ Range[150]],smdQ] (* _Harvey P. Dale_, Jun 20 2021 *)

%o (Magma) a:=[]; for p in PrimesUpTo(700) do v:=[]; for i in [1..#Intseq(p)] do  if Intseq(p)[i] ne 0 then Append(~v,Intseq(p)[i]); end if; end for; if IsPrime(&+[p mod v[u]: u in [1..#v]]) then Append(~a,p); end if; end for; a; // _Marius A. Burtea_, Dec 19 2019

%K nonn,base

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 19 2019