cp's OEIS Frontend

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.

%I A345406 #20 Jul 12 2021 03:39:57
%S A345406 0,1,2,3,4,5,6,7,8,9,90,744,840
%N 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.
%C A345406 The rising factorial d^(c) is defined as d*(d+1)*(d+2)*...*(d+c-1).
%e A345406 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.
%t A345406 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 *)
%o A345406 (C++) #include <iostream>
%o A345406 #include <cmath>
%o A345406 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; }}
%Y A345406 Cf. A014080 (factorions), A265609 (rising factorials), A345405.
%K A345406 nonn,base,fini,more
%O A345406 1,3
%A A345406 _Andrzej Kukla_, Jun 18 2021