A362953 -id:A362953 - cp's OEIS frontend

A362954 Numbers k such that k + the sum of the fourth powers of its digits is again a fourth power.

0, 6047, 7518, 8127, 12207, 25247, 50000, 71966, 77326, 89582, 156156, 376189, 384624, 384640, 599611, 611356, 700158, 794139, 796715, 800558, 1172829, 1329051, 1329324, 1329340, 1488080, 1492525, 1862190, 2546894, 2547885, 5295852, 5302286, 5755548, 6244080, 6246510, 7291980, 7869294

Offset: 0

Will Gosnell and M. F. Hasler, May 09 2023

Karl-Heinz Hofmann, Visualization of n = 0 to 4.

Cf. A000583 (4th powers), A055013 (sum of 4th powers of decimal digits of n).

Cf. A362953 (the same for 3rd powers).

select( {is(n,p=4)=ispower(vecsum([d^p|d<-digits(n)])+n,p)}, [0..10^5])

aupto   = 7869300
A362954 = []
A000583 = set(fp**4 for fp in range(0, int(aupto**(1/4)+3)))
for n in range(0, aupto+1):
    if n + sum(int(digit)**4 for digit in str(n)) in A000583: A362954.append(n)
print(A362954) # Karl-Heinz Hofmann, Jun 02 2023

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

Original entry on oeis.org

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

M. F. Hasler, Jun 15 2023

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

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

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

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]

cp's OEIS Frontend

A362954 Numbers k such that k + the sum of the fourth powers of its digits is again a fourth power.

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