A391636 Integers k such that the sum of the products of each digit of k and the number obtained by removing that digit is equal to k.

36, 360, 1314, 3600, 13140, 36000, 131400, 360000, 1314000, 3600000, 13140000, 36000000, 131400000, 360000000, 1314000000, 3600000000

Offset

1,1

Comments

A088116(k) is the sum of the products of each digit of k and the number obtained by removing that digit, for example, A088116(4567) = 4*567 + 5*467 + 6*457 + 7*456 = 10537. The sequence gives k such that A088116(k) = k.

36*10^j and 1314*10^j are terms for all j >= 0, since:

A088116(36*10^j) = 3*6*10^j + 6*3*10^j = 36*10^j and

A088116(1314*10^j) = 1*314*10^j + 3*114*10^j + 1*134^j + 4*131*10^j = 1314*10^j.

Are there any terms that are not of the form 36*10^j or 1314*10^j, with j >= 0?

Links

Table of n, a(n) for n=1..16.

Example

1314 is a term since 1314 = 1*314 + 3*114 + 1*134 + 4*131.

Mathematica

fsm[k_]:=Module[{kd=IntegerDigits[k], l=IntegerLength[k], sum=0}, Do[sum=sum+kd[[i]]*FromDigits[Drop[kd, {i}]], {i, l}]; sum]; Select[Range[1314000], #==fsm[#]&] (* James C. McMahon, Feb 02 2026 *)

Crossrefs

Cf. A088116, A065759.

Sequence in context: A250422 A223307 A244795 * A392441 A222492 A385023

Adjacent sequences: A391633 A391634 A391635 * A391637 A391638 A391639

Keyword

nonn,base,more

Author

Gonzalo Martínez, Jan 25 2026

Extensions

a(13)-a(16) from Sean A. Irvine, Feb 01 2026

Status

approved