cp's OEIS Frontend

A384444 Positive integers k for which the sum of their digits equals the product of their prime digits.

%I A384444 #11 Jun 20 2025 15:41:26
%S A384444 1,2,3,5,7,10,20,22,30,50,70,100,123,132,200,202,213,220,231,300,312,
%T A384444 321,500,700,1000,1023,1032,1203,1230,1247,1274,1302,1320,1356,1365,
%U A384444 1427,1472,1536,1563,1635,1653,1724,1742,2000,2002,2013,2020,2031,2103,2130,2147
%N A384444 Positive integers k for which the sum of their digits equals the product of their prime digits.
%C A384444 Numbers k for which A007953(k) = A384443(k).
%C A384444 If t is a term then t*10^m is also a term for any positive integer m.
%H A384444 Felix Huber, <a href="/A384444/b384444.txt">Table of n, a(n) for n = 1..10000</a>
%e A384444 1302 is a term, because 1 + 3 + 0 + 2 = 3*2 = 6.
%p A384444 A384444:=proc(n)
%p A384444     option remember;
%p A384444     local k,c;
%p A384444     if n=1 then
%p A384444         1
%p A384444     else
%p A384444         for k from procname(n-1)+1 do
%p A384444             c:=convert(k,'base',10);
%p A384444             if mul(select(isprime,c))=add(c) then
%p A384444                 return k
%p A384444             fi
%p A384444         od
%p A384444     fi;
%p A384444 end proc;
%p A384444 seq(A384444(n),n=1..51);
%t A384444 Select[Range[2147],Total[IntegerDigits[#]]==Times@@Select[IntegerDigits[#],PrimeQ]&] (* _James C. McMahon_, Jun 20 2025 *)
%o A384444 (PARI) isok(k) = my(d=digits(k)); vecprod(select(isprime, d)) == vecsum(d); \\ _Michel Marcus_, Jun 04 2025
%Y A384444 Cf. A002110, A006753, A007947, A007954, A066306, A067077, A384443, A384445, A384505.
%K A384444 nonn,base,easy
%O A384444 1,2
%A A384444 _Felix Huber_, Jun 03 2025