The odd integers unioned with the odd integers times 2^(2k-1) for k = 1, 2, 3,....

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 81, 82

1

Complement of A108269. This sequence answers Stan Wagon’s question “For which positive integers n is there a sum of n consecutive integers that is a perfect square?"

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Stan Wagon, An Odd Consecutive Integer Problem

(Mma) nn = 100; od = Range[1, nn, 2]; Union[od, Flatten[Table[2^i*Range[1, nn/2^i, 2], {i, 1, Log[nn]/Log[2], 2}]]]

Cf. A108269.

nonn

T. D. Noe, Oct 16 2016