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A236507 Smallest k that is a concatenation of two numbers x and y where x^2 + y^2 = n^2. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A002144, A236383.

Sequence in context: A300024 A069534 A237416 * A031140 A095973 A299970

Adjacent sequences:  A236504 A236505 A236506 * A236508 A236509 A236510

KEYWORD

nonn,base,less

AUTHOR

Michel Lagneau, Jan 27 2014

STATUS

approved

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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)