what is the record for most consecutives games with at least 1 rebound

LeBron James has the most games with 1+ rebound, with 1,557 games.

Interpreted as:

What is the record for most consecutives regular-season games by a player with at least 1 rebound?

	NAME	GP	REB	MPG	PPG	RPG	APG	SPG	BPG	FGM	FGA	FG%	3PM	3PA	3P%	FTM	FTA	FT%	TS%	OREB	DREB	TPG	MIN	PTS	AST	STL	BLK	TOV	PF	+/-
1	LeBron James L. James	1,557	11,731	37.8	27.0	7.5	7.4	1.5	0.7	9.9	19.6	50.6	1.6	4.7	35.0	5.5	7.5	73.7	59.0	1.2	6.4	3.5	58,880	42,091	11,546	2,334	1,146	5,463	2,775	+7406
2	Dirk Nowitzki D. Nowitzki	1,508	11,489	34.0	20.9	7.6	2.4	0.8	0.8	7.4	15.7	47.1	1.3	3.4	38.0	4.8	5.5	87.9	57.7	1.0	6.6	1.6	51,213	31,497	3,640	1,210	1,276	2,485	3,583	+6554
3	Karl Malone K. Malone	1,475	14,968	37.2	25.0	10.1	3.6	1.4	0.8	9.2	17.8	51.6	0.1	0.2	27.4	6.6	8.9	74.2	57.7	2.4	7.7	3.1	54,850	36,925	5,248	2,087	1,145	4,524	4,576	+3014
4	Vince Carter V. Carter	1,467	6,606	30.8	17.2	4.5	3.2	1.0	0.6	6.2	14.3	43.7	1.5	4.1	37.1	3.3	4.1	79.7	53.6	1.1	3.4	1.7	45,219	25,295	4,639	1,494	865	2,537	3,898	+2019
5	Kevin Garnett K. Garnett	1,455	14,662	34.6	17.9	10.1	3.7	1.3	1.4	7.2	14.5	49.7	0.1	0.4	27.4	3.4	4.3	79.0	54.6	2.2	7.9	2.2	50,316	26,027	5,438	1,858	2,036	3,174	3,548	+4900
6	Tim Duncan T. Duncan	1,391	15,091	34.0	19.0	10.8	3.0	0.7	2.2	7.4	14.6	50.6	0.0	0.1	17.9	4.2	6.1	69.6	55.1	2.8	8.1	2.4	47,350	26,490	4,223	1,024	3,019	3,381	3,302	+8903
7	Kevin Willis K. Willis	1,382	11,901	27.6	12.4	8.6	1.0	0.7	0.5	5.1	10.5	48.7	0.0	0.1	21.1	2.2	3.1	71.3	52.5	3.0	5.6	1.8	38,088	17,180	1,319	948	744	2,500	4,110	-707
8	Jason Kidd J. Kidd	1,379	8,725	36.1	12.6	6.3	8.7	1.9	0.3	4.5	11.2	40.0	1.4	4.1	34.9	2.2	2.9	78.4	50.7	1.3	5.0	2.9	49,780	17,415	12,013	2,672	445	3,974	2,554	+3886
9	John Stockton J. Stockton	1,361	4,051	32.4	13.4	3.0	10.7	2.2	0.2	4.8	9.3	51.5	0.6	1.5	38.2	3.3	4.0	82.4	60.7	0.7	2.3	2.9	44,068	18,298	14,624	2,986	284	3,927	3,592	+2865
10	Clifford Robinson C. Robinson	1,351	6,306	31.0	14.3	4.7	2.3	1.0	1.0	5.4	12.3	43.8	0.9	2.6	35.6	2.6	3.8	69.0	51.2	1.4	3.3	1.8	41,947	19,373	3,061	1,384	1,376	2,466	4,100	+841
11	Chris Paul C. Paul	1,328	5,978	33.8	17.1	4.5	9.3	2.0	0.2	6.0	12.9	46.9	1.4	3.7	36.9	3.6	4.2	87.0	58.0	0.6	3.9	2.3	44,859	22,680	12,320	2,670	217	3,048	3,128	+6097
12	Kobe Bryant K. Bryant	1,324	7,047	36.4	25.2	5.3	4.7	1.5	0.5	8.8	19.6	44.7	1.4	4.2	33.0	6.3	7.5	83.6	54.9	1.1	4.2	3.0	48,235	33,382	6,270	1,923	633	3,985	3,324	+4218
13	Paul Pierce P. Pierce	1,312	7,527	34.5	19.9	5.7	3.6	1.3	0.6	6.5	14.7	44.5	1.6	4.4	36.8	5.2	6.5	80.6	56.7	0.8	4.9	2.7	45,308	26,095	4,659	1,734	739	3,499	3,589	+3279
14	Reggie Miller R. Miller	1,285	4,182	34.7	18.5	3.3	3.0	1.1	0.2	6.0	12.8	47.1	1.8	4.7	39.3	4.6	5.1	88.7	61.2	0.7	2.6	1.8	44,640	23,728	3,917	1,432	291	2,286	2,528	+1845
15	Gary Payton G. Payton	1,272	5,269	35.8	16.7	4.1	6.8	1.8	0.2	6.7	14.3	46.5	0.9	2.7	31.7	2.5	3.4	72.7	52.7	1.1	3.0	2.3	45,503	21,191	8,678	2,346	278	2,936	3,088	+2029
16	Charles Oakley C. Oakley	1,265	12,206	31.7	9.8	9.6	2.5	1.1	0.3	3.8	8.1	47.1	0.1	0.2	25.3	2.1	2.8	76.0	52.6	3.1	6.5	2.2	40,151	12,401	3,209	1,350	383	2,773	4,392	+235
17	A.C. Green	1,256	9,473	29.0	9.8	7.5	1.1	0.8	0.4	3.6	7.3	49.4	0.1	0.4	25.5	2.5	3.4	73.4	55.7	2.7	4.9	1.1	36,371	12,298	1,396	1,025	544	1,430	2,420	-377
18	Ray Allen R. Allen	1,255	5,272	35.9	19.0	4.2	3.4	1.1	0.2	6.6	14.7	45.1	2.3	5.8	40.0	3.4	3.9	89.3	57.9	1.0	3.2	2.1	45,004	23,875	4,254	1,403	237	2,642	2,753	+3326
19	Sam Perkins S. Perkins	1,255	7,666	28.8	12.1	6.1	1.6	0.9	0.7	4.3	9.4	46.0	0.7	1.8	35.9	2.7	3.4	81.1	55.3	1.9	4.3	1.2	36,148	15,179	1,954	1,094	924	1,566	3,136	+1099
20	Carmelo Anthony C. Anthony	1,252	7,808	34.6	22.5	6.2	2.7	1.0	0.5	8.1	18.0	44.7	1.4	3.9	35.6	5.0	6.2	81.4	54.3	1.6	4.7	2.4	43,344	28,204	3,417	1,220	643	3,046	3,530	+1571
21	Otis Thorpe O. Thorpe	1,245	10,367	31.9	14.1	8.3	2.2	0.7	0.4	5.5	10.1	54.6	0.0	0.1	4.7	3.1	4.5	68.6	58.4	2.8	5.6	2.2	39,696	17,568	2,724	836	501	2,759	4,120	-422
22	Dwight Howard D. Howard	1,241	14,627	31.8	15.7	11.8	1.4	0.9	1.8	5.7	9.7	58.7	0.0	0.1	21.4	4.3	7.6	56.7	60.2	3.3	8.4	2.7	39,431	19,483	1,676	1,081	2,228	3,302	3,911	+2884
23	Hakeem Olajuwon H. Olajuwon	1,237	13,747	35.7	21.8	11.1	2.5	1.7	3.1	8.7	17.0	51.2	0.0	0.1	20.2	4.4	6.2	71.2	55.3	3.3	7.9	3.0	44,214	26,946	3,058	2,161	3,825	3,667	4,380	+556
24	Mark Jackson M. Jackson	1,235	4,963	30.8	9.9	4.0	8.1	1.3	0.1	3.8	8.5	44.7	0.6	1.7	33.3	1.7	2.2	76.8	52.2	1.0	3.0	2.5	37,984	12,170	10,043	1,564	114	3,048	2,171	+526
25	Andre Miller A. Miller	1,225	4,795	31.8	12.9	3.9	6.7	1.2	0.2	4.8	10.4	46.0	0.2	0.7	22.2	3.2	3.9	80.8	53.2	1.1	2.8	2.5	38,953	15,839	8,240	1,503	223	3,016	2,775	+924