A236383 -id:A236383 - cp's OEIS frontend

A236507 Smallest k that is a concatenation of two numbers x and y where x^2 + y^2 = n^2.

10, 20, 30, 40, 34, 60, 70, 80, 90, 68, 1100, 1200, 1205, 1400, 1209, 1600, 1508, 1800, 1900, 1216, 2100, 2200, 2300, 2400, 1520, 1024, 2700, 2800, 2021, 1824, 3100, 3200, 3300, 1630, 2128, 3600, 1235, 3800, 1536, 2432, 4009, 4200, 4300, 4400, 2736, 4600, 4700

Offset: 1

Michel Lagneau, Jan 27 2014

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,...

			a(37) = 1235 because 1235 is the concatenation of 12 and 35, and 12^2 + 35^2 = 1369 = 37^2.

Michel Lagneau, Table of n, a(n) for n = 1..500

Cf. A002144, A236383.

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:

cp's OEIS Frontend

A236507 Smallest k that is a concatenation of two numbers x and y where x^2 + y^2 = n^2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple