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

1,2

Links

Table of n, a(n) for n=1..60.

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

Cf. A203565, A352461, A352464.

Sequence in context: A321990 A076641 A076643 * A326402 A127204 A331626

Adjacent sequences: A352460 A352461 A352462 * A352464 A352465 A352466

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Mar 17 2022

Status

approved