A257650 Squares that are the concatenation of two Pythagorean integers a and b with a^2 + b^2 = c^2 (a and b are without any left-hand zeros).

1024, 4096, 5776, 240100, 540225, 960400, 1500625, 2160900, 26357956, 688012900, 843612025, 1548029025, 2296038889, 2353026064, 2679097600, 2752051600, 3374448100, 4300080625, 209862023449, 389412192841, 662078397124, 839448093796, 1557648771364, 2558976102400

Offset

1,1

Comments

Squares that can be split up in more than one way appear only once.

Links

Reiner Moewald and Giovanni Resta, Table of n, a(n) for n = 1..156 (first 22 terms from Reiner Moewald)

Example

1024 = 32^2 and 10^2 + 24^2 = 26^2.

Prog

(Python)
import math
list = []
for i in range(1, 100000):
   a = i*i
   b = str(a)
   for j in range(1, len(b)):
      a_1 = b[:j]
      a_2 = b[j:]
      c = int(a_1)*int(a_1)+int(a_2)*int(a_2)
      sqrt_c = math.isqrt(c)
      if (sqrt_c * sqrt_c == c) and (int(a_2[:1]) > 0):
         if not a in list:
            list.append(a)
print(list)

Crossrefs

Sequence in context: A195093 A258734 A195234 * A255664 A358001 A195004

Adjacent sequences: A257647 A257648 A257649 * A257651 A257652 A257653

Keyword

nonn,base

Author

Reiner Moewald, Jul 25 2015

Status

approved