OFFSET
1,1
COMMENTS
This sequence is the union of three subsequences:
a subsequence of trivial numbers with n different from 5k, k=1,2,... and y = 0. This subsequence is 10, 20, 30, 40, 60, 70, 80, 90, 1100, 1200, 1400, 1600, 1800, 1900, 2100,...
a subsequence with n = 5k and y different from 0. This subsequence is 34, 68, 1209, 1216, 1520, 1824, 2128, 2432, 2736, 1448, 3344, 3648, 1663, 4256, 2172, 4864, 1384,...
a subsequence with n different from 5k and y different from 0. This subsequence is 1205, 1508, 1024, 2021, 1630, 1235, 1636, 4009,... for n = 13, 17, 26, 29, 34, 37, 39, 41,... Except for the prime 5, the prime indices of this subsequence are Pythagorean primes 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173,... (A002144) and the composite indices are multiples of Pythagorean primes:
26 = 2*13, 34=2*17, 51 = 3*17, 52 = 4*13, 58 = 2*29,...
LINKS
Michel Lagneau, Table of n, a(n) for n = 1..500
EXAMPLE
a(37) = 1235 because 1235 is the concatenation of 12 and 35, and 12^2 + 35^2 = 1369 = 37^2.
MAPLE
with(numtheory):
for n from 1 to 50 do:
ii:=0:
for k from 1 to 10^8 while(ii=0)do :
x:=convert(k, base, 10):n1:=nops(x):
if irem(n1, 2)=0
then
s:=sum('x[i]*10^(i-1) ', 'i'=1..n1/2):
s1:=sum('x[j]*10^(j-n1/2-1) ', 'j'=n1/2+1..n1):
if s^2+s1^2 = n^2
then
ii:=1: printf(`%d, `, k):
else
fi:
fi:
od:
od:
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
Michel Lagneau, Jan 27 2014
STATUS
approved