A224515 -id:A224515 - cp's OEIS frontend

A224511 Roots of squares generated in A221643. That is, S = i^2 XOR (i+1)^2; increment i; if S is a square then square root of S is appended to a(n). Initially i=0. XOR is the binary logical exclusive-or operator.

1, 5, 3, 9, 7, 13, 11, 21, 17, 15, 43, 45, 29, 19, 41, 25, 23, 59, 39, 27, 35, 33, 31, 85, 37, 61, 51, 53, 47, 81, 79, 49, 55, 121, 83, 75, 57, 73, 77, 67, 65, 63, 71, 69, 125, 89, 87, 123, 105, 107, 95, 101, 163, 93, 91, 99, 97, 349, 243, 103, 169, 109, 233, 115, 119, 171

Offset: 1

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Alex Ratushnyak, Apr 08 2013

nonn
base
less

Conjecture: this is a permutation of odd numbers.

b(n) = (a(n)-1)/2 begins: 0, 2, 1, 4, 3, 6, 5, 10, 8, 7, 21, 22, 14, 9, 20, 12, 11, 29, 19, 13, 17.

Cf. A221643, A224515.

import math
for i in range(1<<16):
    s = (i*i) ^ ((i+1)*(i+1))
    r = int(math.sqrt(s));
    if s == r*r:
        print(r, end=', ')

cp's OEIS Frontend

A224511 Roots of squares generated in A221643. That is, S = i^2 XOR (i+1)^2; increment i; if S is a square then square root of S is appended to a(n). Initially i=0. XOR is the binary logical exclusive-or operator.

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