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

1, 2, 3, 5, 7, 10, 20, 22, 30, 50, 70, 100, 123, 132, 200, 202, 213, 220, 231, 300, 312, 321, 500, 700, 1000, 1023, 1032, 1203, 1230, 1247, 1274, 1302, 1320, 1356, 1365, 1427, 1472, 1536, 1563, 1635, 1653, 1724, 1742, 2000, 2002, 2013, 2020, 2031, 2103, 2130, 2147

Offset: 1

Author

Felix Huber, Jun 03 2025

Keywords

• nonn
• base
• easy

Comments

Numbers k for which A007953(k) = A384443(k).

If t is a term then t*10^m is also a term for any positive integer m.

Examples

			1302 is a term, because 1 + 3 + 0 + 2 = 3*2 = 6.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A006753, A007947, A007954, A066306, A067077, A384443, A384445, A384505.

Programs

Maple

A384444:=proc(n)
    option remember;
    local k,c;
    if n=1 then
        1
    else
        for k from procname(n-1)+1 do
            c:=convert(k,'base',10);
            if mul(select(isprime,c))=add(c) then
                return k
            fi
        od
    fi;
end proc;
seq(A384444(n),n=1..51);

Mathematica

Select[Range[2147],Total[IntegerDigits[#]]==Times@@Select[IntegerDigits[#],PrimeQ]&] (* James C. McMahon, Jun 20 2025 *)

PARI

isok(k) = my(d=digits(k)); vecprod(select(isprime, d)) == vecsum(d); \\ Michel Marcus, Jun 04 2025