MindSports

Here are the series of successively better rational approximations of the first 100 non-squares.
Carréphobic numbers are given in red.

2	3	5	6	7	8	10	11	12	13	14	15	17	18	19	20	21	22	23	24	26	27	28	29	30
31	32	33	34	35	37	38	39	40	41	42	43	44	45	46	47	48	50	51	52	53	54	55	56	57
58	59	60	61	62	63	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	82	83	84
85	86	87	88	89	90	91	92	93	94	95	96	97	98	99	101	102	103	104	105	106	107	108	109	110