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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A276512 A023792 A221221 * A179309 A032946 A273738

Adjacent sequences:  A178351 A178352 A178353 * A178355 A178356 A178357

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Dec 21 2010

STATUS

approved

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Last modified April 16 10:13 EDT 2021. Contains 343036 sequences. (Running on oeis4.)