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

1,2

Comments

A179309 is included in this sequence.

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

Links

Carole Dubois, Table of n, a(n) for n = 1..34794

Carole Dubois, Scatterplot of a(n) vs Sum of powers in definition.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A002113, A179309.

Sequence in context: A023792 A221221 A355224 * A179309 A032946 A273738

Adjacent sequences: A178351 A178352 A178353 * A178355 A178356 A178357

Keyword

nonn,base

Author

Michel Lagneau, Dec 21 2010

Status

approved