cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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

Views

Author

Keywords

Crossrefs

Programs

  • Mathematica
    Table[ PrimePi[ n*10^12 ], {n, 1, 15}]
  • PARI
    a(n)=primepi(10^12*n) \\ Charles R Greathouse IV, Apr 29 2015

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jan 29 2003

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

Extensions

a(7)-a(10) from Robert G. Wilson v, Feb 04 2006

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

Views

Author

Robert G. Wilson v and Jeff Burch, Jan 29 2003

Keywords

Crossrefs

Programs

  • Mathematica
    Table[ PrimePi[ n*10^13 ], {n, 1, 9}]
  • PARI
    a(n)=primepi(10^13*n) \\ Charles R Greathouse IV, Apr 29 2015

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

Views

Author

Gus Wiseman, May 30 2024

Keywords

Examples

			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}
		

Crossrefs

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.
Counting zeros instead of all bits gives A372474, firsts of A035103.
Counting ones instead of all bits gives A372517, firsts of A014499.
For primes between powers of 2:
- sum A293697
- length A036378
- min A104080 or A014210
- max A014234, delta A013603
For squarefree numbers between powers of 2:
- sum A373123
- length A077643, run-lengths of A372475
- min A372683, delta A373125, indices A372540
- max A372889, delta A373126, indices A143658
For squarefree numbers between primes:
- sum A373197
- length A373198 = A061398 - 1
- min A000040
- max A112925, opposite A112926

Programs

  • Mathematica
    Table[PrimePi[If[n==1,2,NextPrime[2^n]]],{n,30}]
  • PARI
    a(n) = primepi(nextprime(2^n)); \\ Michel Marcus, May 31 2024

Formula

a(n>1) = A007053(n) + 1.
a(n) = A000720(A104080(n)).
prime(a(n)) = A104080(n).
prime(a(n)) - 2^n = A092131(n).

Extensions

More terms from Michel Marcus, May 31 2024
Previous Showing 31-40 of 140 results. Next