login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270343 Numbers n that end with ( sum of digits of n )^2. 1
0, 1, 81, 3144, 3256, 6225, 6484, 6576, 7121, 7529, 7676, 9100, 9324, 9361, 9729, 9784, 12144, 12256, 15225, 15484, 15576, 16121, 16529, 16676, 18100, 18324, 18361, 18729, 18784, 21144, 21256, 24225, 24484, 24576, 25121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

All terms end with a digit from the set S = {0,1,4,5,6,9}.

The sum of the digits of the numbers repeat and also change with regular intervals. For example the sum of the digits S1 = {12,16,15,22,24,11,23,26,10,18,19,27,28} which is followed by 3144 to 8784, 12144 to 18784, 21144 to 27784, 30144 to 36784. Again S2 = {21,25,15,22,24,11,23,26,10,18,19,27,28} is followed by 39441 to 45784,48441 to 54784, 57441 to 67784, 66441 to 72784. It can be seen that a set containing 13 elements repeats itself for 4 consecutive ranges.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..10000

Soumil Mandal, Graph Of Sum Of Digits

Soumil Mandal, Graph Of Cumulative Sums

EXAMPLE

For n=3256, sum of digits is 16 and 16^2 is 256.

For n=7121, sum of digits is 11 and 11^2 is 121.

For n=18784, sum of digits is 22 and 22^2 is 484.

MAPLE

P:= proc(q) local a, b, k, n; for n from 1 to q do a:=0; b:=n;

for k from 1 to ilog10(n)+1 do a:=a+(b mod 10); b:=trunc(b/10); od;

if a^2=(n mod 10^(ilog10(a^2)+1)) then print(n); fi; od; end: P(10^6); # Paolo P. Lava, Mar 17 2016

MATHEMATICA

Select[Range[0, 20000], Function[n, Function[k, If[n >= k, FromDigits@ Take[#, -IntegerLength@ k] == k, False]][Total[#]^2] &@ IntegerDigits@ n]] (* Michael De Vlieger, Mar 15 2016 *)

PROG

(PARI) isok(n) = {sds = sumdigits(n)^2; nbs = #Str(sds); ((n - sds) % 10^nbs) == 0; } \\ Michel Marcus, Mar 16 2016

(Python)

for i in range(0, 200000):

    res = pow((sum(map(int, str(i)))), 2)

    if(i%pow(10, len(str(res)))==res):print(i)

# Soumil Mandal, Mar 17 2016

CROSSREFS

Cf. A003226, A008851, A018247, A118881.

Sequence in context: A295252 A295651 A143652 * A236894 A231768 A017797

Adjacent sequences:  A270340 A270341 A270342 * A270344 A270345 A270346

KEYWORD

base,nonn,easy

AUTHOR

Soumil Mandal, Mar 15 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 October 26 10:52 EDT 2020. Contains 338027 sequences. (Running on oeis4.)