Monday, December 11, 2006

Square Root Pyramid

A pyramid of the first N-squared digits, in base N, of the square root of N, for N from 0 to 16. (Zero is the invisible tip of the pyramid.)

1

10
11

120
120
212

2000
0000
0000
0000

21042
23240
11324
10400
13441

224103
122055
214532
500432
040411
055205

2434330
6654246
0332333
2613624
6615662
3042200
2313525

26501171
46376357
14441054
57542331
56522537
23707267
54056504
47352046

300000000
000000000
000000000
000000000
000000000
000000000
000000000
000000000
000000000

3162277660
1683793319
9889354443
2718533719
5551393252
1682685750
4852792594
4386392382
2134424810
8379300295

33534781483
717A7320678
4A648721160
78472490883
50711AAA317
71131198955
78303107503
840A8013430
0673437A404
62566345368
2625A487045

3569B73BB715
20982A77945A
A3BB17635011
92060BB2B865
653562BB160B
2A5895A91201
04455152A928
267A19329301
B385BB7A27BA
A83137645955
A11453342438
1592370B2862

37B451C466C91
C692520276B60
1158204643121
B597312B9A462
685019B818044
9C69977518B63
4AA094637945A
607987B0A8895
A04895559325C
694CC113CC18C
10C13613A4678
780810436A304
C444929321751

3A55171DC9B9AB
C1505DB61C58B9
4A85C4983087BC
89495129278B43
D760C5C74281C4
D24ABC31C9BBD7
3298AC74AC9987
886106165C940B
5588686149DDA4
9B5C372CA5610A
52B2DCB73CB9B1
A95331B3766098
D8319B46873B82
41B128748029D5

3D164BADDB995E9
84D12CE1AB17076
8D2CC6C049774D5
6418C514860B587
83766A469782CA4
86677E93768D36C
71BEA7D17AACCDE
3C1C1DBAE161659
56168CCB271D74A
30A9006CB721246
3E9966E37C64E4C
EAB820D20E30106
2E740319C33E715
799EBA7188333DC
9192126A5127B79

4000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000
0000000000000000

echo 'scale=1000;for(i=2;i<=16;i++){obase=i;sqrt(i)}' | bc | perl -pwe 's/\\\n//;s/\.//' |
#!perl -nw
$l=$.+1; for($i=0;$i<$l*$l;$i+=$l){ print "",(substr$_,$i,$l),"\n" } print "\n";

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