A178360 Numbers n such that d(1)^1 + d(2)^2 + ... + d(p)^p and d(1)^p + d(2)^p-1 +... + d(p)^1 are squares, where d(i), i=1..p, are the digits of n.

1, 4, 9, 10, 40, 90, 100, 148, 400, 838, 841, 900, 1000, 1111, 1440, 4000, 4058, 6430, 7388, 8504, 8668, 8837, 9000, 10000, 10111, 10200, 11011, 11101, 11110, 11215, 12321, 13231, 13333, 13955, 14083, 14403, 14464, 17780, 18480, 18770, 20112, 21012, 21102, 21412, 22322, 22592, 25652, 29522, 30205, 30343, 30441

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..250

Example

841 is in the sequence because  :
8 + 4^2 + 1^3 = 25 = 5^2 ;
8^3 + 4^2 + 1 =  529 = 23^2.

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:s10:=  sqrt(s1):s20:=sqrt(s2): if s10=floor(s10) and s20=floor(s20) then printf(`%d, `, n):else fi:od:

Mathematica

ndnQ[n_]:=Module[{idn=IntegerDigits[n], len=Range[IntegerLength[n]]}, AllTrue[{Sqrt[Total[idn^len]], Sqrt[Total[Reverse[idn]^len]]}, IntegerQ]]; Select[Range[31000], ndnQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 10 2018 *)

Crossrefs

Sequence in context: A178224 A102985 A112401 * A197125 A197129 A115688

Adjacent sequences: A178357 A178358 A178359 * A178361 A178362 A178363

Keyword

nonn,base

Author

Michel Lagneau, Dec 21 2010

Status

approved