# From: Jon Schoenfield (jonscho(AT)hiwaay.net)
# Subject: b-file for A003166
# Date: Fri, 8 May 2009 15:54:51 -0500
# 
# I've = attached a b-file containing all terms in A003166 less than 2^48.  Some 
# observations that allowed a fast search:
# 
# Other than a(1) = 0, all terms in the sequence must, of course, be 
# odd.
# 
# All odd numbers j have the property that j^2 mod 8 = 1, so, in base 2, 
# j^2 (if it's at least 4 digits long) must end in 001, and if it's 
# palindromic, then it must begin with 100, so, for j^2 > 7, we can limit 
# the search to odd numbers j such that j^2 lies in the ranges
# 
#    8 < j^2 < 10,
#    16 < j^2 < 20,
#    32 < j^2 < 40, etc.
# 
# We can cut in half the number of possible values of j needing to be 
# checked if we note further that
# 
# - for integers j such that j^2 mod 16 = 1, j mod 8 = 1 or its 
# complement, 7
# - for integers j such that j^2 mod 16 = 9, j mod 8 = 3 or its 
# complement, 5
# 
# so, for j^2 > 15, we can limit the search to numbers j = 8*k +/- 1 
# (here and below, k is any positive integer) with j^2 starting with 1000, 
# i.e., in the ranges
# 
#      16 < j^2 < 18,
#      32 < j^2 < 36,
#      64 < j^2 < 72, etc.
# 
# and numbers j = 8*k +/- 3 with j^2 starting with 1001, i.e., in the 
# ranges
# 
#      18 < j^2 < 20,
#      36 < j^2 < 40,
#      72 < j^2 < 80, etc.
# 
# Extending this one step further,
# 
# - for integers j such that j^2 mod 32 = 1, j mod 16 = 1 or its 
# complement, 15
# - for integers j such that j^2 mod 32 = 9, j mod 16 = 3 or its 
# complement, 13
# - for integers j such that j^2 mod 32 = 17, j mod 16 = 7 or its 
# complement, 9
# - for integers j such that j^2 mod 32 = 25, j mod 16 = 5 or its 
# complement, 11
# 
# so, for j^2 > 31, we can limit the search to numbers j = 16*k +/- 1 
# with j^2 starting with 10000, i.e., in the ranges
# 
#      32 < j^2 < 34,
#      64 < j^2 < 68,
#      128 < j^2 < 136, etc.,
# 
# numbers j = 16*k +/- 3 with j^2 starting with 10010, i.e., in the 
# ranges
# 
#      36 < j^2 < 38,
#      72 < j^2 < 76,
#      144 < j^2 < 152, etc.,
# 
# numbers j = 16*k +/- 7 with j^2 starting with 10001, i.e., in the 
# ranges
# 
#      34 < j^2 < 36,
#      68 < j^2 < 72,
#      136 < j^2 < 144, etc.,
# 
# and numbers j = 16*k +/- 5 with j^2 starting with 10011, i.e., in the 
# ranges
# 
#      38 < j^2 < 40,
#      76 < j^2 < 80,
#      152 < j^2 < 160, etc.
# 
# (Extending the above by several more steps makes it easy to check all 
# possible values of j up into the trillions.)
# 
# I'm sure the above could all be written much more succinctly!
# 

1 0
2 1
3 3
4 4523
5 11991
6 18197
7 141683
8 1092489
9 3168099
10 6435309
11 12489657
12 17906499
13 68301841
14 295742437
15 390117873
16 542959199
17 4770504939
18 17360493407
19 73798050723
20 101657343993
21 107137400475
22 202491428745
23 1615452642807
24 4902182461643
25 9274278357017
26 12863364360297
27 18242038950999
28 18600264487591
29 25100748703521
30 39192943705973
31 154737433904091