A068880 Smallest n-digit square with property that digits alternate in parity.
1, 16, 121, 1296, 12321, 147456, 1038361, 10929636, 103652761, 1010985616, 10327234129, 101070583056, 1010163694761, 10107210905856, 101030903296569, 1012923810743296, 10101430507492129, 101034169694343076, 1010167692929438121, 10101478149656965696
Offset: 1
Examples
a(4) = 1296 as 1, 2, 9 and 6 have odd and even parity alternately.
Links
- Sean A. Irvine, Table of n, a(n) for n = 1..53 (terms 1..33 from Giovanni Resta)
Programs
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Mathematica
altQ[n_] := n < 10 || Union[ Total /@ Partition[ Mod[ IntegerDigits@n, 2], 2, 1]] == {1}; a[n_] := Block[{r = Ceiling@ Sqrt@ FromDigits[ Mod[Range@ n, 2]]}, While[! altQ[r^2], r++]; r^2]; Array[a, 16] (* Giovanni Resta, Aug 17 2018 *) -
Python
from math import isqrt from itertools import count, islice def allalt(s): es, os, e, o = set(s[::2]), set(s[1::2]), set("02468"), set("13579") return (es <= o and os <= e) or (es <= e and os <= o) def a(n): r = isqrt(int(("10"*n)[:n])) while len(s:=str(r*r)) < n or not allalt(s): r += 1 return int(s) print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Mar 21 2024
Extensions
More terms from Sascha Kurz, Mar 23 2002
a(14)-a(20) from Giovanni Resta, Aug 17 2018