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

0, 210, 66374, 76933, 294137, 722571, 741300, 1023716, 2412593, 3959235, 4022940, 5090402, 6351886, 7821198, 9653864, 11808061, 11814811, 20427955, 24190287, 24239133, 24245187, 33518020, 33532714, 33536551, 39060306, 52476271, 52480534, 69255266, 69265142, 79091461, 89980491, 90147222

Offset: 0

Author

M. F. Hasler, Jun 15 2023

Keywords

• nonn
• base

Crossrefs

Cf. A000584 (4th powers), A055014 (sum of 5th powers of decimal digits).

Cf. A362953 (same for 3rd powers), A362954 (same for 4th powers).

Programs

PARI

is_A362945(n,p=5)=ispower(vecsum([d^p|d<-digits(n)])+n,p)
for(n=0,1e8, is_A362945(n) && print1(n", "))

Python

ispower5 = lambda n: n==round(n**.2)**5
is_A362945 = lambda n: ispower5(sum(int(d)**5 for d in str(n))+n)
def A362945(n, A=[0]):
    while len(A) < n:
        A.append(A[-1]+1)
        while not is_A362945(A[-1]): A[-1]+=1
    return A[n]