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A352463
Numbers k with the property that the product of the digits of k starts k.
1
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
1,2
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Mar 17 2022
STATUS
approved