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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197129 Numbers such that the sum, sum of the squares, and sum of the cubes of the decimal digits are each a perfect square. 1
1, 4, 9, 10, 40, 90, 100, 400, 900, 1000, 1111, 1224, 1242, 1339, 1393, 1422, 1933, 2124, 2142, 2214, 2241, 2412, 2421, 3139, 3193, 3319, 3391, 3913, 3931, 4000, 4122, 4212, 4221, 4444, 4669, 4696, 4966, 6469, 6496, 6649, 6694, 6946, 6964, 9000, 9133, 9313 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each number > 90 contains at least two identical digits because the sequence A197125 contains a subset of numbers all of whose digits are distinct and are all the permutations of 1567890. But 1^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3 = 1926 is not square. Consequently, it is impossible to find numbers > 90 with distinct digits in this sequence.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

A028839 INTERSECT A175396 INTERSECT A197039.

EXAMPLE

4669 is in the sequence because:

4   + 6   + 6   + 9   = 25   = 5^2;

4^2 + 6^2 + 6^2 + 9^2 = 169  = 13^2;

4^3 + 6^3 + 6^3 + 9^3 = 1225 = 35^2.

MAPLE

for n from 1 to 10000 do:l:=evalf(floor(ilog10(n))+1):n0:=n:s1:=0:s2:=0:s3:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10): n0:=v :s1:=s1+u:s2:=s2+u^2:s3:=s3+u^3:od:if sqrt(s1)=floor(sqrt(s1)) and sqrt(s2)=floor(sqrt(s2)) and sqrt(s3)=floor(sqrt(s3))then printf(`%d, `, n): else fi:od:

MATHEMATICA

sdQ[n_]:=Module[{idn=IntegerDigits[n]}, IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Total[idn^2]]]&&IntegerQ[Sqrt[Total[idn^3]]]]; Select[ Range[ 10000], sdQ] (* Harvey P. Dale, Oct 25 2011 *)

PROG

(PARI) is(n)=my(v=eval(Vec(Str(n)))); issquare(sum(i=1, #v, v[i]))&&issquare(sum(i=1, #v, v[i]^2))&&issquare(sum(i=1, #v, v[i]^3)) \\ Charles R Greathouse IV, Oct 10 2011

CROSSREFS

Cf. A028839, A175396, A197039, A197125.

Sequence in context: A112401 A178360 A197125 * A115688 A115710 A082749

Adjacent sequences:  A197126 A197127 A197128 * A197130 A197131 A197132

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Oct 10 2011

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 May 20 03:10 EDT 2019. Contains 323412 sequences. (Running on oeis4.)