A345406 Integers k such that k = d1^(c) + d2^(c) + ... + dc^(c), where d^(c) denotes the rising 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, 90, 744, 840

Offset

1,3

Comments

The rising 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

7^(3) + 4^(3) + 4^(3) = 7*8*9 + 4*5*6 + 4*5*6 = 504 + 120 + 120 = 744, therefore 744 is in the list.

Mathematica

q[n_] := Module[{dig = IntegerDigits[n], nd}, nd = Length[dig]; Sum[(d + nd - 1)!/(d - 1)!, {d, dig}] == n]; Select[Range[0, 1000], q] (* Amiram Eldar, Jun 18 2021 *)

Prog

(C++) #include <iostream>
#include <cmath>
using namespace std; unsigned long long rf(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+=rf(a%10, k); a/=10; }if(p==n){cout<<n<<", "; } p=0; }}

Crossrefs

Cf. A014080 (factorions), A265609 (rising factorials), A345405.

Sequence in context: A024664 A078188 A240511 * A198486 A061805 A280658

Adjacent sequences: A345403 A345404 A345405 * A345407 A345408 A345409

Keyword

nonn,base,fini,more

Author

Andrzej Kukla, Jun 18 2021

Status

approved