A345405 Integers k such that k = (d1)_c + (d2)_c + ... + (dc)_c, where (d)_c denotes the descending factorial of d, c is the length of k and di is the i-th digit of k in base 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 86, 15960

Offset

1,3

Comments

The descending factorial (d)_c is defined as d*(d-1)*(d-2)*...*(d-c+1).

Links

Table of n, a(n) for n=1..13.

Example

(8)_2 + (6)_2 = 8*7 + 6*5 = 56 + 30 = 86, therefore 86 is in the list.

Mathematica

q[n_] := Module[{dig = IntegerDigits[n], nd}, nd = Length[dig]; Sum[d!/(d - nd)!, {d, dig}] == n]; Select[Range[0, 16000], q] (* Amiram Eldar, Jun 18 2021 *)

Prog

(C++) #include <iostream>
#include <cmath>
using namespace std; unsigned long long ff(unsigned long long a, int b){unsigned long long s=1; for(int i=0; i<b; i++){s=s*(a-i); } return s; }int main(int argc, char** argv) {int k, a, p=0; for(unsigned long long n=0; n<=pow(10, 9); n++){k=floor(log10(n))+1; a=n; for(int j=1; j<=k; j++){p+=ff(a%10, k); a/=10; }if(p==n){cout<<n<<", "; } p=0; }}

Crossrefs

Cf. A014080 (factorions), A068424 (descending factorials), A345406.

Sequence in context: A064154 A316147 A080161 * A257554 A270393 A257787

Adjacent sequences: A345402 A345403 A345404 * A345406 A345407 A345408

Keyword

nonn,fini,full,base

Author

Andrzej Kukla, Jun 18 2021

Status

approved