A352463 Numbers k with the property that the product of the digits of k starts k.
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 21, 31, 41, 51, 61, 71, 81, 91, 111, 126, 153, 211, 243, 311, 362, 411, 511, 611, 711, 811, 911, 1111, 1216, 1223, 1232, 1261, 1288, 1359, 1449, 1513, 1531, 1755, 2111, 2413, 2431, 3111, 3612, 3621, 3844, 4111, 5111, 6111, 6728, 7111, 7357, 8111, 9111, 11111, 11278, 11287
Offset: 1
Examples
a(10) = 11 starts with 1, which is the product 1*1; a(20) = 126 starts with 12, which is the product 1*2*6; a(42) = 1755 starts with 175, which is the product ; 1*7*5*5; etc.
Programs
-
Mathematica
q[n_] := Module[{d = IntegerDigits[n], p, dp, ndp}, p = Times @@ d; dp = IntegerDigits[p]; ndp = Length[dp]; dp == d[[1 ;; ndp]]]; Select[Range[12000], q] (* Amiram Eldar, Mar 18 2022 *) -
Python
from math import prod def ok(n): s = str(n); return s.startswith(str(prod(map(int, s)))) print([k for k in range(1, 12000) if ok(k)]) # Michael S. Branicky, Mar 17 2022