login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270926 Numbers n such that n*R(n) can be represented as sum of two nonzero squares, where R(n) is the reverse of the decimal expansion of n. 1
5, 10, 15, 16, 18, 20, 25, 30, 37, 40, 50, 51, 52, 55, 58, 60, 61, 70, 73, 78, 80, 81, 85, 87, 89, 90, 98, 100, 101, 104, 106, 109, 110, 111, 122, 125, 128, 145, 146, 148, 149, 150, 159, 160, 162, 164, 165, 168, 169, 174, 176, 180, 181, 192, 195, 198, 200, 202, 208, 212, 220, 221, 222 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n*R(n) is the square of the hypotenuse of a right angled triangle.

Palindromes of this sequence are 5, 55, 101, 111, 181, 202, 212, 222, 232, 272, 292, 303, 313, 323, 333, 353, 373, ... - Altug Alkan, Mar 26 2016

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000

EXAMPLE

For n=5 R(n)=5 and n*R(n)=25 which is 3^2+4^2.

For n=10 R(n)=1 and n*R(n)=10 which is 1^2+3^2.

For n=58 R(n)=85 and n*R(n)=4930 which is 13^2+69^2.

MAPLE

T:=proc(w) local x, y, z; x:=w; y:=0;

for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10); od; y; end:

P:=proc(q) local a, k, n; for n from 1 to q do a:=n*T(n);

for k from 1 to q do if a-k^2>0 then if type(sqrt(a-k^2), integer) then print(n); break;

fi; fi; od; od; end: P(10^6); # Paolo P. Lava, Mar 30 2016

MATHEMATICA

Select[Range@ 222, Length[PowersRepresentations[# FromDigits@ Reverse@ IntegerDigits@ #, 2, 2] /. {0, _} -> Nothing] > 0 &] (* Michael De Vlieger, Mar 26 2016 *)

PROG

(PARI) isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}

lista(nn) = for(n=1, nn, if(isA000404(n*eval(concat(Vecrev(Str(n))))), print1(n, ", "))); \\ Altug Alkan, Mar 26 2016

(Python)

from sys import version_info

if version_info >= (3, 0):

   xrange = range

def isHypotenuse(num):

    a, b=1, 1

    while((a**2+b**2)<=num):

         while((a**2+b**2)<=num):

              if((a**2+b**2)==num): return 1

              b+=1

         a+=1

         b=1

    return 0

for x in xrange(0, 20000):

    if(isHypotenuse(x*int(str(x)[::-1]))==1):print(x)

    #Soumil Mandal, Mar 27 2016

CROSSREFS

Cf. A000404, A004086, A061205.

Sequence in context: A080949 A313666 A242128 * A317045 A037977 A044845

Adjacent sequences:  A270923 A270924 A270925 * A270927 A270928 A270929

KEYWORD

base,nonn,easy

AUTHOR

Soumil Mandal, Mar 26 2016

EXTENSIONS

More terms from Altug Alkan, Mar 26 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)