For those interested:
Key
1 1 2^1 = 2 (-1)
2 3 2^2 = 4 (-1)
3 7 2^3 = 8 (-1)
4 8 2^4 = 16 (-NO3)
5 21 2^5 = 32 (-NO3,-NO2)
6 49 2^6 = 64 (-NO4)
7 76 2^7 = 128 (-NO5,-NO4,-NO2)___(-NO2)
8 224 2^8 = 256 (-NO5)
9 467 2^9 = 512 (-NO5,-NO4)
10 514 2^10 = 1024 (-NO9)
11 1155 2^11 = 2048 (-NO9,-NO8,-NO7)
12 2683 2^12 = 4096 (-NO10,-NO8,-NO7,*NO3*)
13 5216 2^13 = 8192 (-NO11,-NO9,-NO8,-NO7,-NO5)
14 10544 2^14 = 16384 (-NO12,-NO10,-NO9,-NO7,-NO6,-NO4)
15 26867 2^15 = 32768 (-NO13,+NO11,+NO8) OR (-NO12,-NO10,-NO9,-NO8,-NO4)
16 51510 2^16 = 65536 (-NO14,+NO11,+NO8) OR (-NO13,-NO12,-NO10,-NO9,-NO7,-NO6,-NO3,-NO1)
17 95823 2^17 = 131072 (-NO15,-NO11,-NO8,-NO7,-NO6)___(+NO14,-NO7)
18 198669 2^18 = 262144 (-NO16,+NO11) OR (-NO15,-NO14,-NO13,-NO12,-NO11)
19 357535 2^19 = 524288 (-NO17,NO15,NO11,NO10,*+NO7*)
20 863317 2^20 = 1048576 (-NO18,+NO16,+NO13,+NO11,+NO10,+NO6)
21 1811764 2^21 = 2097152 (-NO19,+NO18,-NO14,-NO12,-N011,-NO10)
22 3007503 2^22 = 4194304 (-NO20,NO17,NO13,+NO10)
23 5598802 2^23 = 8388608 (-NO21,NO19,NO17,NO15,NO13,+NO11,+NO10)
24 14,428,676 2^24 = 16,777,216 (-NO22,+N021,-NO18,+NO13,+NO11) OR (-NO21,-NO18,+NO13,+NO11)
25 33,185,509 2^25 = 33,554,432 (-NO18,-NO16,-NO15,-NO13,*-NO8,-NO5*) OR (-NO23)
26 54,538,862 2^26 = 67,108,864 (-NO24,+NO22,+NO13,+NO12,*+NO9,+NO6)
27 111,949,941 2^27 = 134,217,728 (-NO25,+NO23,+NO21,+NO19,+NO18,+NO13,+NO12,+NO11,)___(+NO24,+NO23,+NO22,+NO21,+NO19,+NO18,+NO)
28 227,634,408 2^28 = 268,435,456 (-NO26,+24,+23,+20,+16,+14,+13,+11,+10,*+7,+6,+5,+3) OR (-NO25,-23,+20,+16,+14,+13,+11,*+10,+7,+6,+5,+3)
29 400,708,894 2^29 = 536,870,912 (-NO27,-21,+17,+14,+12,+10,*+8,+4,+3,+2,+1)
30 1,033,162,084 2^30 = 1,073,741,824 (-NO25,-22,-21,-19,-17,-16,-13,-12,*-9,-7,-5)
31 2,102,388,551 2^31 = 2,147,483,648 (-NO25,-23,-21,-20,-12,-11,*-7,-5,-4,-3,-)
32 3,093,472,814 2^32 = 4,294,967,296 (-NO30,-26,-25,-24,-23,-21,*+17,+15,+13,+10,**+9,+5,+3,+2,+1) OR (-NO30,-27,+22,+21,*+17,+15,+13,+10,**+9,+5,+3,+2,+1)
33 7,137,437,912 2^33 = 8,589,934,592 (-NO30,-28,-26,-25,-23,-20,*-17,-16,-14,-12,-11,**+7,+6,+4,+3)
34 14,133,072,157 2^34 = 17,179,869,184 (-NO31,-29,-28,-26,-24,-23,-20,*-19,-17,-14,-13,-11,-10,**-9,-7,-6,-5,-1-)
35 20,112,871,792 2^35 = 34,359,738,368 (-NO33,-32,-30#,-28,-24,-21,-20,*+17,+12,*+8,+6,+5,+4)
36 42,387,769,980 2^36 = 68,719,476,736 (-NO34,-33#,-29,-24,-23,*+17,+11,+9,+6--2)
37 100,251,560,595 2^37 = 137,438,953,472 (-NO35,-31#,-29,-27,-23,-20,*+18,+16,+14,+13,+11,**+10)
38 146,971,536,592 2^38 = 274,877,906,944 (-NO36,-35,-34,-32,-31,-30,-29#,+28,+27,+21,+20,*-21K) OR (-NO36,-35,-34,-33,#+29,+28,+27,+21,+20,*-21K)
39 323,724,968,937 2^39 = 549,755,813,888 (-NO37,-36,-34,-31,-30#,+28--23,*+17,+16,+10,-023)
40 1,003,651,412,950 2^40 = 1,099,511,627,776 (-NO36,-34,-33,-30,#-28,-24,-23,-21,-20,*-18,-17,-15,-14,-12,*+)
41 1,458,252,205,147 2^41 = 2,199,023,255,552 (-NO39,-37,-35,-34,-31,#+26,+25,+23,+21,*-341K)
42 2,895,374,552,463 2^42 = 4,398,046,511,104 **(-NO40,-38,-36,-35,-34,-32,-31,-30,#-28,--25,-22,*+300K)
43 7,409,811,047,825 2^43 = 8,796,093,022,208 (-NO40,-38,-33,-31,-30,#-26,-23,-22,-20,*-19,-15K)
44 15,404,761,757,071 2^44 = 17,592,186,044,416 (-NO40,-39,$-38,-37,-36,-35,-34,-32,-30,#-27,-26,-23,-21,-20,*+600K)
45 19,996,463,086,597 2^45 = 35,184,372,088,832 (-NO43,-42,-40,-39,-38,-36,$-30,#+27,+25,+21,*-800K) OR (-NO43,-42,-41,$+37,+36,-1BILION*)
46 51,408,670,348,612 2^46 = 70,368,744,177,664 (-NO44,-40,$-37,-36,-35,-34,-33,-31,#+59M*)
47 119,666,659,114,170 2^47 = 140,737,488,355,328 (-NO44,-41,-40,$-37,-35,-33,*+200M)
48 191,206,974,700,443 2^48 = 281,474,976,710,656 (-NO46,-44,-41,$-36,-35,-32,-30,*+399M*)
49 409,118,905,032,525 2^49 = 562,949,953,421,312 (-NO47,-43,-41,-40,-39,$-38,-37,-35,-31,-30,*+700M*)
50 611,140,496,167,764 2^50 = 1,125,899,906,842,624 (-NO48,-47,-46,-44,-42$,-37,-35,-33,-32,-31,-30#,-26*+3M*)
51 2,058,769,515,153,876 2^51 = 2,251,799,813,685,248 (-NO47,-45,-43,-42,-41,-40,-39#,-36*+2BILION*)
52 4,216,495,639,600,700 2^52 = 4,503,599,627,370,496 (-NO48,-42,-40#,-36,-35,-34,-33,-31,-30*,+600M*)
53 6,763,683,971,478,124 2^53 = 9,007,199,254,740,992 (-NO50,-49,-48,-47$,-46,-45,-44,-43,-40#,+550BILION*)
54 9,974,455,244,496,710 2^54 = 18,014,398,509,481,984 (-NO52,-51,-50,-47$,-44#,-38,-35,-32*,-29,-27,-25,-22,-200k*)
55 30,045,390,491,869,460 2^55 = 36,028,797,018,963,968 (-NO52,-50$,-48,-46,-41#,+100BILLION)
56 44,218,742,292,676,575 2^56 = 72,057,594,037,927,936 (-NO54,-53,-49$,-47,-46,-45,-"[43]"42,-41,-40,-39#,+200BILION*)
57 138,245,758,910,846,492 2^57 = 144,115,188,075,855,872 (-NO52,-50$,-47,-46,-44,-43,-41*,-38*+30BILL)
58 199,976,667,976,342,049 2^58 = 288,230,376,151,711,744 (-NO56,-53,-52,-51,-48,-47$,-43,-41#,-40*)
59 2^59 = 576,460,752,303,423,488
60 2^60 = 1,152,921,504,606,846,976
* point of brute force