[seqfan] Re: sqrt digits last few values

[Russ Cox]

I agree.

$ ./recalc
A004542 sqrt(2) base 5
BC:
1,2,0,1,3,4,2,0,2,0,4,1,3,0,0,0,0,3,4,2,0,4,2,2,3,2,4,1,3,
3,2,3,4,2,2,3,1,2,0,3,1,0,3,0,3,2,1,0,3,0,4,1,2,4,1,0,4,1,
1,4,4,2,1,3,2,1,4,2,1,1,1,0,3,2,0,2,0,3,2,1,3,4,0,0,1,0,0,
2,3,0,1,1,3,1,2,1,3,0,0,
OEIS:
1,2,0,1,3,4,2,0,2,0,4,1,3,0,0,0,0,3,4,2,0,4,2,2,3,2,4,1,3,
3,2,3,4,2,2,3,1,2,0,3,1,0,3,0,3,2,1,0,3,0,4,1,2,4,1,0,4,1,
1,4,4,2,1,3,2,1,4,2,1,1,1,0,3,2,0,2,0,3,2,1,3,4,0,0,0,4,4,
2,4,1,0,0,4,3,2,1,0,2,0,

A004582 sqrt(8) base 7
BC:
2,5,5,4,1,0,2,4,2,3,4,2,2,4,6,5,5,2,1,5,3,0,1,4,2,0,2,4,0,
3,5,3,6,5,5,1,1,3,1,1,0,1,1,5,3,2,2,5,5,1,3,4,3,5,0,4,5,6,
5,3,4,6,0,3,4,4,0,5,5,1,4,6,3,3,4,3,4,5,2,0,5,4,1,6,1,1,4,
3,3,2,2,3,3,3,4,0,1,1,3,
OEIS:
2,5,5,4,1,0,2,4,2,3,4,2,2,4,6,5,5,2,1,5,3,0,1,4,2,0,2,4,0,
3,5,3,6,5,5,1,1,3,1,1,0,1,1,5,3,2,2,5,5,1,3,4,3,5,0,4,5,6,
5,3,4,6,0,3,4,4,0,5,5,1,4,6,0,1,1,3,4,5,1,0,3,2,1,6,5,6,5,
6,4,2,1,3,0,6,2,6,4,2,2,

A004583 sqrt(8) base 8
BC:
2,6,5,0,1,1,7,1,4,6,3,7,6,3,5,7,1,4,4,4,1,0,5,4,5,7,5,4,2,
3,3,1,5,6,5,2,2,5,3,7,2,3,7,0,7,2,6,7,5,4,0,5,6,5,0,4,4,7,
3,5,2,0,4,6,3,5,5,0,5,7,2,6,2,0,5,4,0,6,3,1,6,3,1,0,5,2,4,
5,3,7,4,4,0,6,0,2,0,7,2,
OEIS:
2,6,5,0,1,1,7,1,4,6,3,7,6,3,5,7,1,4,4,4,1,0,5,4,5,7,5,4,2,
3,3,1,5,6,5,2,2,5,3,7,2,3,7,0,7,2,6,7,5,4,0,5,6,5,0,4,4,7,
3,5,2,0,4,6,3,5,4,

A004584 sqrt(8) base 9
BC:
2,7,4,0,8,2,7,1,2,2,6,8,3,3,1,6,0,7,3,1,7,3,6,0,4,4,7,3,4,
5,7,7,6,6,1,8,0,5,3,2,5,4,5,1,6,4,4,1,6,4,1,2,3,8,2,2,2,2,
2,4,4,6,7,4,4,6,3,2,0,6,5,0,7,6,1,1,1,7,6,3,7,7,5,8,2,1,8,
4,0,0,6,5,1,5,8,5,5,0,7,
OEIS:
2,7,4,0,8,2,7,1,2,2,6,8,3,3,1,6,0,7,3,1,7,3,6,0,4,4,7,3,4,
5,7,7,6,6,1,8,0,5,3,2,5,4,5,1,6,4,4,1,6,4,1,2,3,8,2,2,2,2,
2,4,4,6,7,3,8,0,7,

A004588 sqrt(10) base 5
BC:
3,0,4,0,1,2,0,2,4,3,2,3,4,1,4,2,0,3,1,1,3,2,2,1,1,2,2,0,1,
2,0,0,3,2,3,4,4,4,4,4,2,3,4,3,3,2,4,4,2,4,0,4,4,1,4,3,0,3,
1,4,4,1,2,3,3,1,3,3,4,2,4,2,2,2,0,4,0,3,3,3,4,1,2,1,4,2,4,
3,3,0,2,3,4,4,1,4,0,3,1,
OEIS:
3,0,4,0,1,2,0,2,4,3,2,3,4,1,4,2,0,3,1,1,3,2,2,1,1,2,2,0,1,
2,0,0,3,2,3,4,4,4,4,4,2,3,4,3,3,2,4,4,2,4,0,4,4,1,4,3,0,3,
1,4,4,1,2,3,3,1,3,3,4,2,4,2,2,2,0,4,0,3,3,3,4,1,2,1,4,2,3,
3,0,2,3,4,2,4,1,2,4,4,1,

$ cat recalc
#!/bin/sh

nl='
'

run() {
	echo "$1 sqrt($2) base $3"
	echo "BC:"
	echo "val=$2; scale=100; obase=$3; ibase=$3; sqrt(val)" |
		bc -l -q |
		tr -d "$nl\\" |
		awk '{print substr($0, 1, 100)}' |
		sed 's/\.//; s/./&, /g' |
		fmt -88 |
		sed 's/, /,/g'
	echo "OEIS:"
	curl -s "http://oeis.org/search?q=id:$1&fmt=text" | grep '%[STU]' |
		awk '{print $3}' |
		tr -d ",$nl" |
		awk '{print substr($0, 1, 100)}' |
		sed 's/\.//; s/./&, /g' |
		fmt -88 |
		sed 's/, /,/g'
	echo
}

run A004542 2 5
run A004582 8 7
run A004583 8 8
run A004584 8 9
run A004588 10 5
$