A387866 - OEIS

A387866

Numbers that can be split into two numbers whose products of digits are equal.

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 200, 212, 221, 224, 236, 248, 300, 313, 326, 331, 339, 400, 414, 422, 428, 441, 500, 515, 551, 600, 616, 623, 632, 661, 700, 717, 771, 800, 818, 824, 842, 881, 900, 919, 933, 991, 1000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Leading zeros are allowed only for the second number, e.g., 1001 split into 10 and 01.

Numbers with more than 1 decimal digit '0' are terms. - Chai Wah Wu, Sep 17 2025

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

221 is a term since A007954(2) = A007954(21);

1001 is a term since A007954(10) = A007954(01);

1050 is a term since A007954(10) = A007954(50);

14224 is a term since A007954(142) = A007954(24).

MAPLE

filter:= proc(n) local L, i;

L:= convert(n, base, 10);

ormap(i -> convert(L[1..i], `*`) = convert(L[i+1..-1], `*`), [$1..nops(L)-1])

end proc:

select(filter, [$10 .. 2000]); # Robert Israel, Sep 18 2025

MATHEMATICA

Select[Range[1000], Sum[Boole[Product[Part[(digits=IntegerDigits[#]), i], {i, k}]==Product[Part[digits, i], {i, k+1, IntegerLength[#]}]], {k, IntegerLength[#]-1}]>0 &]

PROG

(Python)

from math import prod

def ok(n):

d = list(map(int, str(n)))

return any(prod(d[:i]) == prod(d[i:]) for i in range(1, len(d)))

print([k for k in range(1001) if ok(k)]) # Michael S. Branicky, Sep 12 2025

(PARI) isok(k) = my(d=digits(k)); for (i=2, #d, if (prod(j=1, i-1, d[j]) == prod(j=i, #d, d[j]), return(1)); ); \\ Michel Marcus, Sep 12 2025

CROSSREFS

Cf. A007954, A067042, A083967, A238237, A387867.

Sequence in context: A044851 A276769 A160861 * A302575 A302801 A067042

Adjacent sequences: A387863 A387864 A387865 * A387867 A387868 A387869

KEYWORD

nonn,base,easy

AUTHOR

Stefano Spezia, Sep 10 2025

STATUS

approved