OFFSET
1,2
COMMENTS
Written in base twenty the numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J, 60D, 6EA8, 4F100, 4F101, E57CAI, JA8FAB, 9DEC7H2, B86BB0HH.
If a(28) exists, it is greater than 20^11.
Sequence is finite. Since k*19^k < 20^(k-1) for k >= 157, all terms must have less than 157 base-20 digits. 20*m is a term if and only if 20*m+1 is a term. - Chai Wah Wu, Apr 20 2022
LINKS
Eric Weisstein's World of Mathematics, Narcissistic Number
EXAMPLE
2413 is in the sequence because 2413 is 60D in base 20 (D stands for 13) and 6^3 + 0^3 + 13^3 = 2413. (The exponent 3 is the number of base-20 digits.)
MATHEMATICA
Select[Range[10^6], # == Total[ IntegerDigits[#, 20]^IntegerLength[#, 20]] &]
PROG
(PARI) isok(m) = my(d=digits(m, 20)); sum(k=1, #d, d[k]^#d) == m; \\ Michel Marcus, Mar 19 2022
(Python)
from itertools import islice, combinations_with_replacement
from sympy.ntheory.factor_ import digits
def A351374_gen(): # generator of terms
for k in range(1, 157):
a = tuple(i**k for i in range(20))
yield from (x[0] for x in sorted(filter(lambda x:x[0] > 0 and tuple(sorted(digits(x[0], 20)[1:])) == x[1], \
((sum(map(lambda y:a[y], b)), b) for b in combinations_with_replacement(range(20), k)))))
CROSSREFS
KEYWORD
base,nonn,more,fini
AUTHOR
Giovanni Corbelli, Mar 18 2022
EXTENSIONS
a(28)-a(30) from Chai Wah Wu, Apr 20 2022
STATUS
approved