cp's OEIS Frontend

A225303 Primes of the form p + (product of digits of p), where p is a prime.

%I A225303 #13 Sep 21 2019 14:35:15
%S A225303 29,47,67,101,103,107,109,181,251,293,307,331,347,401,409,431,443,457,
%T A225303 491,503,509,547,593,601,607,631,653,659,673,701,709,743,809,823,827,
%U A225303 839,907,929,971,977,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091
%N A225303 Primes of the form p + (product of digits of p), where p is a prime.
%C A225303 Primes generated by A157677.
%H A225303 Robert Israel, <a href="/A225303/b225303.txt">Table of n, a(n) for n = 1..10000</a>
%e A225303 29 is in the list since 29 = 23 + (2*3).
%p A225303 f:= proc(n) local L,v;
%p A225303   if not isprime(n) then return NULL fi;
%p A225303   L:= convert(n,base,10);
%p A225303   if member(0,L) then return n fi;
%p A225303   v:= n + convert(L,`*`);
%p A225303   if isprime(v) then v else NULL fi
%p A225303 end proc:
%p A225303 N:= 2000: # to get all terms <= N
%p A225303 S:= {}:
%p A225303 for n from 3 by 2 to N do
%p A225303   v:= f(n);
%p A225303   if v <> NULL and v <= N then S:= S union {v} fi;
%p A225303 od:
%p A225303 sort(convert(S,list));# _Robert Israel_, Jun 25 2019
%t A225303 Sort[DeleteDuplicates[Select[Table[p=Prime[n]; p+Times@@IntegerDigits[p], {n,175}],PrimeQ]]]
%t A225303 Select[Table[p+Times@@IntegerDigits[p],{p,Prime[Range[ 200]]}], PrimeQ]// Union (* _Harvey P. Dale_, Sep 21 2019 *)
%Y A225303 Cf. A157677.
%K A225303 nonn,base
%O A225303 1,1
%A A225303 _Jayanta Basu_, May 05 2013
%E A225303 1049,1051,1061,1063,1069 and 1087 inserted by _Robert Israel_, Jun 25 2019