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A270343 Numbers n that end with ( sum of digits of n )^2. 1

%I

%S 0,1,81,3144,3256,6225,6484,6576,7121,7529,7676,9100,9324,9361,9729,

%T 9784,12144,12256,15225,15484,15576,16121,16529,16676,18100,18324,

%U 18361,18729,18784,21144,21256,24225,24484,24576,25121

%N Numbers n that end with ( sum of digits of n )^2.

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

%C 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.

%H Paolo P. Lava, <a href="/A270343/b270343.txt">Table of n, a(n) for n = 1..10000</a>

%H Soumil Mandal, <a href="https://github.com/soumilmandal/DOCUMENTS/blob/master/TRENCHIC/trenchic.png">Graph Of Sum Of Digits</a>

%H Soumil Mandal, <a href="https://github.com/soumilmandal/DOCUMENTS/blob/master/TRENCHIC/CumulativeSums.png">Graph Of Cumulative Sums</a>

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

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

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

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

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

%p 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

%t 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 *)

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

%o (Python)

%o for i in range(0,200000):

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

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

%o # _Soumil Mandal_, Mar 17 2016

%Y Cf. A003226, A008851, A018247, A118881.

%K base,nonn,easy

%O 1,3

%A _Soumil Mandal_, Mar 15 2016

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Last modified November 27 06:49 EST 2020. Contains 338678 sequences. (Running on oeis4.)