A257297 a(n) = (initial digit of n) * (n with initial digit removed).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 1, 2, 3

Offset

0,13

Comments

The initial 100 terms match those of A035930 (maximal product of any two numbers whose concatenation is n) and also those of A171765 (product of digits of n, or 0 for n<10), and except for initial terms, also A007954 (product of decimal digits of n) and A115300 (greatest digit of n * least digit of n).

Iterations of this map always end in 0, since a(n) < n. Sequence A257299 lists numbers for which these iterations reach 0 in exactly 9 steps, with the additional constraint of having each time a different initial digit.

If "initial" is replaced by "last" in the definition (A257850), then we get the same values up to a(100), but (10, 20, 30, ...) for n = 101, 102, 103, ..., again different from each of the 4 other sequences mentioned in the first comment. - M. F. Hasler, Sep 01 2021

Links

Table of n, a(n) for n=0..103.

Formula

For 1 <= m <= 9 and n < 10^k, a(m*10^k + n) = m*n.

Example

For n<10, a(n) = n*0 = 0, since removing the initial and only digit leaves nothing, i.e., zero (by convention).
a(10) = 1*0 = 0, a(12) = 1*2 = 2, ..., a(20) = 2*0 = 0, a(21) = 2*1 = 2, a(22) = 2*2 = 4, ...
a(99) = 9*9 = 81, a(100) = 1*00 = 0, a(101) = 1*01 = 1, ..., a(123) = 1*23, ...

Maple

a:= n-> `if`(n<10, 0, (s-> parse(s[1])*parse(s[2..-1]))(""||n)):
seq(a(n), n=0..120);  # Alois P. Heinz, Feb 12 2024

Mathematica

Table[Times@@FromDigits/@TakeDrop[IntegerDigits@n, 1], {n, 0, 103}] (* Giorgos Kalogeropoulos, Sep 03 2021 *)

Prog

(PARI) apply( {A257297(n)=vecprod(divrem(n, 10^logint(n+!n, 10)))}, [0..111]) \\ Edited by M. F. Hasler, Sep 01 2021
(Python)
def a(n): s = str(n); return 0 if len(s) < 2 else int(s[0])*int(s[1:])
print([a(n) for n in range(104)]) # Michael S. Branicky, Sep 01 2021

Crossrefs

Cf. A257850, A007954, A035930, A080464, A115300, A169669, A111707, A088117, A187844.

Sequence in context: A257850 A080464 A171765 * A035930 A347470 A088117

Adjacent sequences: A257294 A257295 A257296 * A257298 A257299 A257300

Keyword

nonn,base,easy

Author

M. F. Hasler, May 10 2015

Extensions

a(101..103) corrected by M. F. Hasler, Sep 01 2021

Status

approved