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A362945 Numbers k such that k + the sum of the fifth powers of its digits is again a fifth power.

%I A362945 #9 Jun 27 2025 21:42:25
%S A362945 0,210,66374,76933,294137,722571,741300,1023716,2412593,3959235,
%T A362945 4022940,5090402,6351886,7821198,9653864,11808061,11814811,20427955,
%U A362945 24190287,24239133,24245187,33518020,33532714,33536551,39060306,52476271,52480534,69255266,69265142,79091461,89980491,90147222
%N A362945 Numbers k such that k + the sum of the fifth powers of its digits is again a fifth power.
%o A362945 (PARI) is_A362945(n,p=5)=ispower(vecsum([d^p|d<-digits(n)])+n,p)
%o A362945 for(n=0,1e8, is_A362945(n) && print1(n", "))
%o A362945 (Python)
%o A362945 ispower5 = lambda n: n==round(n**.2)**5
%o A362945 is_A362945 = lambda n: ispower5(sum(int(d)**5 for d in str(n))+n)
%o A362945 def A362945(n, A=[0]):
%o A362945     while len(A) < n:
%o A362945         A.append(A[-1]+1)
%o A362945         while not is_A362945(A[-1]): A[-1]+=1
%o A362945     return A[n]
%Y A362945 Cf. A000584 (4th powers), A055014 (sum of 5th powers of decimal digits).
%Y A362945 Cf. A362953 (same for 3rd powers), A362954 (same for 4th powers).
%K A362945 nonn,base
%O A362945 0,2
%A A362945 _M. F. Hasler_, Jun 15 2023