cp's OEIS Frontend

A342944 Numbers m such that d(1)^0 + d(2)^1 + ... + d(k)^(k-1) = d(1)! + d(2)! + ... + d(k)!, where d(i), i=1..k, are the digits of m.

%I A342944 #19 May 22 2021 04:34:59
%S A342944 1,11,12,111,121,133,202,1020,1111,1211,1331,1403,2021,2030,2120,2220,
%T A342944 2305,2413,3012,3102,3115,3202,3215,3322,3335,4033,4123,4223,4434,
%U A342944 10165,10201,10210,10300,10533,11065,11111,11200,12065,12111,12200,13050,13265,13311
%N A342944 Numbers m such that d(1)^0 + d(2)^1 + ... + d(k)^(k-1) = d(1)! + d(2)! + ... + d(k)!, where d(i), i=1..k, are the digits of m.
%e A342944 2413 is in this sequence because 2^0 + 4^1 + 1^2 + 3^3 = 2! + 4! + 1! + 3! = 33.
%t A342944 Select[Range@20000,Total[(a=IntegerDigits@#)^Range[0,Length@a-1]]==Total[a!]&] (* _Giorgos Kalogeropoulos_, Mar 30 2021 *)
%o A342944 (Python)
%o A342944 from math import factorial
%o A342944 def digfac(s): return sum(factorial(int(d)) for d in s)
%o A342944 def digpow(s): return sum(int(d)**i for i, d in enumerate(s))
%o A342944 def aupto(limit):
%o A342944   alst = []
%o A342944   for k in range(1, limit+1):
%o A342944     s = str(k)
%o A342944     if digpow(s) == digfac(s): alst.append(k)
%o A342944   return alst
%o A342944 print(aupto(14000)) # _Michael S. Branicky_, Mar 30 2021
%o A342944 (PARI) is(n) = my(d = digits(n)); sum(i = 1, #d, d[i]!) == sum(i = 1, #d, d[i]^(i-1)) \\ _David A. Corneth_, Mar 30 2021
%Y A342944 Cf. A009994, A342945, A342826, A178354.
%K A342944 nonn,base
%O A342944 1,2
%A A342944 _Carole Dubois_, Mar 30 2021