OFFSET
1,2
COMMENTS
If k has an odd number of digits, all digits after the first digit are paired; see first example below.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..114
EXAMPLE
75625 is a term because partitioning its digits as (7)(56)(25), taking the square root of each part and truncating, and then concatenating the results, gives floor(sqrt(7))|floor(sqrt(56))|floor(sqrt(25)) = 275 = sqrt(75625);
180625 is a term because floor(sqrt(18))|floor(sqrt(06))|floor(sqrt(25)) = 425 = sqrt(180625).
MATHEMATICA
#^2 & /@ Select[Range[10^4], And[Mod[#, 10] != 0, FromDigits@ Map[Floor@ Sqrt@ FromDigits@ # &, Partition[PadLeft[#, 2 Ceiling[Length@ #/2]], 2, 2]] &@ IntegerDigits[#^2] == #] &] (* Michael De Vlieger, Nov 23 2017 *)
PROG
(PARI) is(n) = if(issquare(n) == 0||n % 10 == 0, return(0)); my(sq = i = 0, cn = n); while(cn > 0, sq += 10^i * sqrtint(cn % 100); cn \= 100; i++); sq ^ 2 == n \\ David A. Corneth, Jan 18 2018
(Python)
import math
for k in range(1, 1000000000):
p = 0
z = 0
n = k*k
while n >= 100:
z = z + int(math.floor(math.sqrt(n % 100)) * math.pow(10, p))
n = int((n - (n % 100)) / 100)
p = p + 1
z = z + int(math.floor(math.sqrt(n)) * math.pow(10, p))
if z == k and k % 10 > 0:
print(k * k, k)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reiner Moewald, Nov 01 2017
STATUS
approved