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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.

%I A178354 #21 Mar 25 2021 05:08:10
%S A178354 1,2,3,4,5,6,7,8,9,10,11,22,33,44,55,66,77,88,99,100,101,110,111,120,
%T A178354 121,130,131,140,141,150,151,160,161,170,171,180,181,190,191,202,212,
%U A178354 222,232,242,252,262,272,282,292,303,313,323,333,343,353,363,373,383,393,404,414,424,434,444,454
%N 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.
%C A178354 A179309 is included in this sequence.
%C A178354 All palindromes are in this sequence. - _Harvey P. Dale_, Mar 03 2013
%H A178354 Carole Dubois, <a href="/A178354/b178354.txt">Table of n, a(n) for n = 1..34794</a>
%H A178354 Carole Dubois, <a href="/A178354/a178354.jpg">Scatterplot of a(n) vs Sum of powers in definition.</a>
%e A178354 14603 is in the sequence because :
%e A178354 1 + 4^2 + 6^3 + 0^4 + 3^5 = 3 + 0^2 + 6^3 + 4^4 + 1^5 = 476.
%p A178354 with(numtheory):for n from 1 to 50000 do:l:=length(n):n0:=n:s1:=0:s2:=0:for
%p A178354   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:
%p A178354   if s1=s2 then printf(`%d, `,n):else fi:od:
%t A178354 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 *)
%o A178354 (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
%o A178354 (Python)
%o A178354 def digpow(s): return sum(int(d)**i for i, d in enumerate(s, start=1))
%o A178354 def aupto(limit):
%o A178354   alst = []
%o A178354   for k in range(1, limit+1):
%o A178354     s = str(k)
%o A178354     if digpow(s) == digpow(s[::-1]): alst.append(k)
%o A178354   return alst
%o A178354 print(aupto(454)) # _Michael S. Branicky_, Mar 23 2021
%Y A178354 Cf. A002113, A179309.
%K A178354 nonn,base
%O A178354 1,2
%A A178354 _Michel Lagneau_, Dec 21 2010