A273190 -id:A273190 - cp's OEIS frontend

A273191 a(n) is the length of the n-th run of A273190.

1, 1, 1, 6, 1, 3, 4, 2, 6, 1, 7, 4, 4, 9, 1, 10, 4, 8, 9, 3, 14, 2, 12, 9, 7, 34, 7, 11, 16, 4, 20, 5, 17, 14, 8, 24, 1, 23, 12, 14, 23, 3, 28, 8, 20, 21, 9, 30, 4, 28, 17, 15, 32, 2, 34, 13, 23, 28, 8, 38, 7, 31, 24, 16, 40, 1, 41, 18, 24, 37, 7

Offset: 1

Alec Jones, May 17 2016

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A273190.

import Data.List (group)
a273191 n = a273191_list !! (n - 1)
a273191_list = (map length . group) $ map a273190 [0..]
-- Peter Kagey, Jun 07 2016

Length /@ Split@ Table[Count[Range[0, n - 1], m_ /; IntegerQ@ Sqrt[m + n]], {n, 0, 10^3}] (* Michael De Vlieger, May 24 2016 *)

A273185 Start with a(0) = 0. Thereafter a(n) is the number of m < n with the property that a(m) + n is a perfect square.

Original entry on oeis.org

0, 1, 0, 1, 2, 0, 0, 1, 3, 4, 0, 0, 1, 1, 1, 6, 6, 0, 0, 2, 0, 1, 1, 2, 8, 9, 0, 1, 1, 0, 2, 0, 1, 1, 4, 12, 12, 2, 0, 0, 1, 1, 0, 2, 0, 2, 1, 7, 15, 17, 0, 0, 2, 0, 0, 1, 1, 1, 2, 0, 2, 1, 10, 19, 22, 0, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 14

Offset: 0

Alec Jones, May 17 2016

			a(3) = 1 because 3 + a(1) is a perfect square.
a(4) = 2 because 4 + a(0) and 4 + a(2) are perfect squares.

Peter Kagey, Table of n, a(n) for n = 0..10000

Cf. A273190.

int n = 1000;
int[] terms = new int[n];
for (int i = 0; i < n; i++) {
     for (int j = 0; j < i; j++) {
          if (Math.sqrt(i+terms[j]) == Math.floor(Math.sqrt(i+terms[j]))) {
               terms[i]++;
          }
     }
     System.out.print(terms[i] + ", ");
}

a = {0}; Do[AppendTo[a, Count[a + n, k_ /; IntegerQ@ Sqrt@ k]], {n, 79}]; a (* Michael De Vlieger, May 25 2016 *)

cp's OEIS Frontend

A273191 a(n) is the length of the n-th run of A273190.

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