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A300160 Quasi-narcissistic numbers: k-digit numbers n whose sum of k-th powers of their digits is equal to n +- 1. 1
35, 75, 528757, 629643, 688722, 715469, 31672867, 44936324, 63645890, 63645891, 71419078, 73495876, 1136483324, 310374095702, 785103993880, 785103993881, 989342580966, 23046269501054, 37434032885798, 50914873393416, 75759895149717, 4020913800954247 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..38 (full sequence)
EXAMPLE
35 is in the sequence because 3^2 + 5^2 = 34 = 35 - 1.
31672867 is in the sequence because 3^8 + 1^8 + 6^8 + 7^8 + 2^8 + 8^8 + 6^8 + 7^8 = 31672868 = 31672867 + 1.
MAPLE
P:=proc(q) local a, k, n;
for n from 1 to q do a:=convert(n, base, 10);
a:=add((a[k])^nops(a), k=1..nops(a));
if a=n-1 or a=n+1 then print(n); fi; od; end: P(10^6);
MATHEMATICA
Select[Range[10^6], Abs[# - Total[IntegerDigits[#]^IntegerLength[#]]] == 1 &] (* Michael De Vlieger, Feb 28 2018 *)
PROG
(Python)
from itertools import combinations_with_replacement
A300160_list = []
for k in range(1, 16):
a = [i**k for i in range(10)]
for b in combinations_with_replacement(range(10), k):
y = sum(map(lambda y:a[y], b))
for x in (y-1, y+1):
if x > 0 and tuple(int(d) for d in sorted(str(x))) == b:
A300160_list.append(x)
print(sorted(A300160_list)) # John Drake, Mar 14 2023
CROSSREFS
Cf. A005188.
Sequence in context: A043205 A043985 A254443 * A257750 A257751 A259282
KEYWORD
nonn,base,fini,full
AUTHOR
Paolo P. Lava, Feb 27 2018
EXTENSIONS
a(13)-a(22) from Giovanni Resta, Feb 27 2018
STATUS
approved

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Last modified July 13 17:35 EDT 2024. Contains 374284 sequences. (Running on oeis4.)