A300160 Quasi-narcissistic numbers: k-digit numbers n whose sum of k-th powers of their digits is equal to n +- 1.

35, 75, 528757, 629643, 688722, 715469, 31672867, 44936324, 63645890, 63645891, 71419078, 73495876, 1136483324, 310374095702, 785103993880, 785103993881, 989342580966, 23046269501054, 37434032885798, 50914873393416, 75759895149717, 4020913800954247

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

Adjacent sequences: A300157 A300158 A300159 * A300161 A300162 A300163

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