A178354 Numbers m such that d(1)^1 + d(2)^2 + ... + d(p)^p = d(1)^p + d(2)^(p-1) +... + d(p)^1, where d(i), i=1..p, are the digits of m.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 101, 110, 111, 120, 121, 130, 131, 140, 141, 150, 151, 160, 161, 170, 171, 180, 181, 190, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454

Offset: 1

Author

Michel Lagneau, Dec 21 2010

Keywords

• nonn
• base

Comments

A179309 is included in this sequence.

All palindromes are in this sequence. - Harvey P. Dale, Mar 03 2013

Examples

			14603 is in the sequence because :
1 + 4^2 + 6^3 + 0^4 + 3^5 = 3 + 0^2 + 6^3 + 4^4 + 1^5 = 476.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..34794
• Carole Dubois, Scatterplot of a(n) vs Sum of powers in definition.

Crossrefs

Cf. A002113, A179309.

Programs

Maple

with(numtheory):for n from 1 to 50000 do:l:=length(n):n0:=n:s1:=0:s2:=0:for
  m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s1:=s1+u^(l-m+1):s2:=s2+u^m:od:
  if s1=s2 then printf(`%d, `,n):else fi:od:

Mathematica

drQ[n_]:=Module[{id=IntegerDigits[n],len},len=Length[id];Total[ id^Range[ len]] == Total[id^Range[len,1,-1]]]; Select[Range[500],drQ] (* Harvey P. Dale, Aug 04 2018 *)

PARI

isok(m) = my(d=digits(m), p=#d); sum(k=1, p, d[k]^k) == sum(k=1, p, d[k]^(p-k+1)); \\ Michel Marcus, Mar 22 2021

Python

def digpow(s): return sum(int(d)**i for i, d in enumerate(s, start=1))
def aupto(limit):
  alst = []
  for k in range(1, limit+1):
    s = str(k)
    if digpow(s) == digpow(s[::-1]): alst.append(k)
  return alst
print(aupto(454)) # Michael S. Branicky, Mar 23 2021