A362953 Numbers N such that N + the sum of the cubes of its digits is again a third power.

0, 34, 352, 540, 1167, 1942, 2176, 3312, 4093, 5454, 8019, 9380, 12025, 12130, 13068, 13158, 15344, 15991, 16279, 16675, 21149, 22699, 22789, 30988, 32257, 32365, 35238, 37883, 37955, 41866, 45549, 54523, 57906, 58530, 62579, 72588, 83692, 83782, 89604, 102952

Offset

0,2

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000

Karl-Heinz Hofmann, Visualization of n = 0 to 11.

Example

The sum of the cubes of the digits of N = 34 is 3^3 + 4^3 = 27 + 64 = 91; added to the number N itself yields  125 which is again a cube, 5^3. Therefore 34 is in this sequence.

Prog

(PARI) select( {is(n, p=3)=ispower(vecsum([d^p|d<-digits(n)])+n, p)}, [0..10^5])
(Python)
aupto = 103000
A362953 = []
A000578 = set(cu**3 for cu in range(0, int(aupto**(1/3)+3)))
for n in range(0, aupto+1):
    if n + sum(int(digit)**3 for digit in str(n)) in A000578: A362953.append(n)
print(A362953) # Karl-Heinz Hofmann, May 24 2023

Crossrefs

Cf. A000578 (the cubes), A055012 (sum of cubes of decimal digits of n).

Cf. A362954 (the same for 4th powers).

Sequence in context: A059338 A301954 A368719 * A244881 A296833 A202413

Adjacent sequences: A362950 A362951 A362952 * A362954 A362955 A362956

Keyword

nonn,base

Author

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

Status

approved