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 [dead link]
Soumil Mandal, Graph Of Cumulative Sums [dead link]
EXAMPLE
For k=3256, sum of digits is 16 and 16^2 is 256.
For k=7121, sum of digits is 11 and 11^2 is 121.
For k=18784, sum of digits is 22 and 22^2 is 484.
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 *)
esdQ[n_]:=Module[{idn=IntegerDigits[n], idn2=IntegerDigits[ Total[ IntegerDigits[ n]]^2]}, Take[ idn, -Length[idn2]]==idn2]; Select[ Range[ 0, 26000], esdQ]//Quiet (* Harvey P. Dale, Jan 01 2022 *)
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
KEYWORD
base,nonn,easy
AUTHOR
Soumil Mandal, Mar 15 2016
STATUS
approved