A380854 Integers m for which m = Sum (d_i + 1)^k, where m is k decimal digits long and d_i are the digits of m.

141, 251, 560, 664807556, 424710875510, 863812804425, 137134427278403350052, 366828486147473227474, 186740753582576522645847734

Offset: 1

Author

Chai Wah Wu, Feb 06 2025

Keywords

• nonn
• more
• base

Examples

			664807556 is a term since it has 9 digits and (6+1)^9+(6+1)^9+(4+1)^9+(8+1)^9+(0+1)^9+(7+1)^9+(5+1)^9+(5+1)^9+(6+1)^9 = 664807556.
		

Crossrefs

Cf. A005188, A261433, A380810.

Programs

Python

from itertools import chain, combinations_with_replacement, count, islice
def A380854_gen(): # generator of terms
    yield from chain.from_iterable(sorted(map(lambda s:sum((d+1)**l for d in s),sorted(filter(lambda s:tuple(sorted(map(int,str(m:=sum((d+1)**l for d in s)))))==s and 10**l>m>=10**(l-1),combinations_with_replacement(range(10),l))))) for l in count(1))
A380854_list = print(list(islice(A380854_gen(),8)))

Extensions

a(1)-a(3) from Paolo P. Lava

a(9) from Chai Wah Wu, Feb 07 2025