A038821
Number of primes less than n*10^12.
Original entry on oeis.org
37607912018, 73301896139, 108340298703, 142966208126, 177291661649, 211381427039, 245277688804, 279010070811, 312600354108, 346065536839, 379418886337, 412671294782, 445831610611, 478907544860, 511905471132
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A080122,
A080123,
A080124,
A080125,
A080126,
A080127,
A080128,
A080129.
A080123
Number of primes less than n*10^14.
Original entry on oeis.org
3204941750802, 6270424651315, 9287441600280, 12273824155491, 15237833654620, 18184255291570, 21116208911023, 24035890368161, 26944926466221, 29844570422669, 32735816605908, 35619471693548
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080124,
A080125,
A080126,
A080127,
A080128,
A080129.
A080124
Number of primes less than n*10^15.
Original entry on oeis.org
29844570422669, 58478215681891, 86688602810119, 114630988904000, 142377417196364, 169969662554551, 197434994078331, 224792606318600, 252056733453928, 279238341033925, 306346140642929, 333387204489157
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080123,
A080125,
A080126,
A080127,
A080128,
A080129.
A080125
Number of primes less than n*10^16.
Original entry on oeis.org
279238341033925, 547863431950008, 812760276789503, 1075292778753150, 1336094767763971, 1595534099589274, 1853851099626620, 2111215026220444, 2367751438410550, 2623557157654233, 2878709063250915, 3133269657307298
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080123,
A080124,
A080126,
A080127,
A080128,
A080129.
A080126
Number of primes less than n*10^17.
Original entry on oeis.org
2623557157654233, 5153329362645908, 7650011911220803, 10125681208311322, 12585956566571620, 15034102021263820, 17472251499627256, 19901908567967065, 22324189231374849, 24739954287740860
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080123,
A080124,
A080125,
A080127,
A080128,
A080129.
A080127
Number of primes less than n*10^18.
Original entry on oeis.org
24739954287740860, 48645161281738535, 72254704797687083, 95676260903887607, 118959989688273472, 142135049412622144, 165220513980969424, 188229829247429504, 211172979243258278
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080123,
A080124,
A080125,
A080126,
A080128,
A080129.
A080128
Number of primes less than n*10^19.
Original entry on oeis.org
234057667276344607, 460637655126005490, 684559920583084690, 906790515105576571, 1127779923790184543, 1347790196060095447, 1566992840325479804, 1785508810123564582, 2003427950419417330
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080123,
A080124,
A080125,
A080126,
A080127,
A080129.
A080129
Number of primes less than n*10^20.
Original entry on oeis.org
2220819602560918840, 4374267703076959271, 6503696293016202398, 8617821096373621600, 10720710117789005897, 12814731195053369962, 14901434779964228982, 16981914723713251575, 19056983802675654255, 21127269486018731928
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080122,
A080123,
A080124,
A080125,
A080126,
A080127,
A080128,
A116356.
A080122
Number of primes less than n*10^13.
Original entry on oeis.org
346065536839, 675895909271, 1000121668853, 1320811971702, 1638923764567, 1955010428258, 2269432871304, 2582444113487, 2894232250783, 3204941750802, 3514687156436, 3823561506566, 4131641836725, 4438993433550, 4745670621117
Offset: 1
Cf.
A038801,
A028505,
A038812,
A038813,
A038814,
A038815,
A038816,
A038817,
A038818,
A038819,
A038820,
A038821,
A080123,
A080124,
A080125,
A080126,
A080127,
A080128,
A080129.
A372684
Least k such that prime(k) >= 2^n.
Original entry on oeis.org
1, 3, 5, 7, 12, 19, 32, 55, 98, 173, 310, 565, 1029, 1901, 3513, 6543, 12252, 23001, 43391, 82026, 155612, 295948, 564164, 1077872, 2063690, 3957810, 7603554, 14630844, 28192751, 54400029, 105097566, 203280222, 393615807, 762939112, 1480206280, 2874398516, 5586502349
Offset: 1
The numbers prime(a(n)) together with their binary expansions and binary indices begin:
2: 10 ~ {2}
5: 101 ~ {1,3}
11: 1011 ~ {1,2,4}
17: 10001 ~ {1,5}
37: 100101 ~ {1,3,6}
67: 1000011 ~ {1,2,7}
131: 10000011 ~ {1,2,8}
257: 100000001 ~ {1,9}
521: 1000001001 ~ {1,4,10}
1031: 10000000111 ~ {1,2,3,11}
2053: 100000000101 ~ {1,3,12}
4099: 1000000000011 ~ {1,2,13}
8209: 10000000010001 ~ {1,5,14}
16411: 100000000011011 ~ {1,2,4,5,15}
32771: 1000000000000011 ~ {1,2,16}
65537: 10000000000000001 ~ {1,17}
131101: 100000000000011101 ~ {1,3,4,5,18}
262147: 1000000000000000011 ~ {1,2,19}
524309: 10000000000000010101 ~ {1,3,5,20}
1048583: 100000000000000000111 ~ {1,2,3,21}
2097169: 1000000000000000010001 ~ {1,5,22}
4194319: 10000000000000000001111 ~ {1,2,3,4,23}
8388617: 100000000000000000001001 ~ {1,4,24}
The opposite (greatest k such that prime(k) <= 2^n) is
A007053.
Positions of first appearances in
A035100.
The distance from prime(a(n)) to 2^n is
A092131.
For primes between powers of 2:
For squarefree numbers between powers of 2:
For squarefree numbers between primes:
-
Table[PrimePi[If[n==1,2,NextPrime[2^n]]],{n,30}]
-
a(n) = primepi(nextprime(2^n)); \\ Michel Marcus, May 31 2024