A028505 -id:A028505 - cp's OEIS frontend

A038811 Duplicate of A028505.

25, 46, 62, 78, 95, 109, 125, 139, 154, 168, 184, 196, 211, 222, 239, 251, 266, 278, 290

Offset: 1

dead

A038822 Number of primes between 100n and 100n+99.

25, 21, 16, 16, 17, 14, 16, 14, 15, 14, 16, 12, 15, 11, 17, 12, 15, 12, 12, 13, 14, 10, 15, 15, 10, 11, 15, 14, 12, 11, 12, 10, 11, 15, 11, 14, 13, 12, 11, 11, 15, 9, 16, 9, 11, 12, 12, 12, 8, 15, 12, 11, 10, 10, 13, 13, 12, 10, 16, 7, 12, 11, 13, 15, 8, 11, 10, 12, 12, 13, 9, 10

Offset: 0

Jeff Burch

nonn

The number k first occurs in century A186311(k).

			a(3) = 16 because there are 16 primes between 300 and 399 (namely, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397).
a(4) = 17 because there are 17 primes between 400 and 499 (401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499).

George P. Loweke, The Lore of Prime Numbers. New York: Vantage Press (1982): 91.

T. D. Noe, Table of n, a(n) for n = 0..9999

Cf. A028505.
Cf. A181098 (centuries without primes).
Cf. A186393-A186408 (centuries having 1 to 16 primes), A186509 (17 primes).
Cf. A094892, A098592.

with(numtheory); A038822 := n->pi(100*n+99)-pi(100*n); seq(A038822(k), k=0..100); # Wesley Ivan Hurt, Oct 03 2013

Table[PrimePi[100n + 99] - PrimePi[100n], {n, 0, 71}]
Differences[PrimePi[100 Range[0,100]]] (* Harvey P. Dale, Feb 18 2021 *)

a(n)=sum(i=100*n,100*n+99,isprime(i)) \\ Charles R Greathouse IV, Apr 28 2015

a(n)= my(r=0, p=100*n, q=p+99); while((p=nextprime(p+1))<=q, r+=isprime(p)); r; \\ Ruud H.G. van Tol, Nov 17 2024

a(n) = pi(100n+99) - pi(100n). - Wesley Ivan Hurt, Oct 03 2013

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

A038801 Number of primes less than 10n.

Original entry on oeis.org

4, 8, 10, 12, 15, 17, 19, 22, 24, 25, 29, 30, 31, 34, 35, 37, 39, 41, 42, 46, 46, 47, 50, 52, 53, 55, 57, 59, 61, 62, 63, 66, 66, 68, 70, 72, 73, 75, 77, 78, 80, 81, 82, 85, 87, 88, 91, 92, 93, 95, 97, 97, 99, 99, 101, 102, 104, 106, 107, 109, 111, 114, 114, 115, 118, 120

Offset: 1

Jeff Burch

nonn

For almost all n, that is for a set of density 1, a(n) = a(n-1), and in all cases a(n) <= a(n-1) + 4. - Charles R Greathouse IV, Aug 27 2014

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A028505, A038812, A038813, A038814, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Table[ PrimePi[ n*10 ], {n, 1, 66}] (* Robert G. Wilson v *)

a(n)=primepi(10*n) \\ Charles R Greathouse IV, Aug 27 2014

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

A038812 Number of primes less than 1000n.

Original entry on oeis.org

168, 303, 430, 550, 669, 783, 900, 1007, 1117, 1229, 1335, 1438, 1547, 1652, 1754, 1862, 1960, 2064, 2158, 2262, 2360, 2464, 2564, 2668, 2762, 2860, 2961, 3055, 3153, 3245, 3340, 3432, 3538, 3638, 3732, 3824, 3923, 4017, 4107, 4203, 4291, 4392, 4494

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038813, A038814, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*1000 ], {n, 1, 45}]
```

a(n)=primepi(1000*n) \\ Charles R Greathouse IV, Apr 29 2015

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

A038813 Number of primes less than 10000n.

Original entry on oeis.org

1229, 2262, 3245, 4203, 5133, 6057, 6935, 7837, 8713, 9592, 10453, 11301, 12159, 13010, 13848, 14683, 15497, 16342, 17170, 17984, 18807, 19618, 20437, 21221, 22044, 22837, 23642, 24432, 25224, 25997, 26800, 27608, 28404, 29182, 29977

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038814, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^4 ], {n, 1, 30}]
```

a(n)=primepi(10000*n) \\ Charles R Greathouse IV, Apr 29 2015

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

A038814 Number of primes less than 100000n.

Original entry on oeis.org

9592, 17984, 25997, 33860, 41538, 49098, 56543, 63951, 71274, 78498, 85714, 92938, 100021, 107126, 114155, 121127, 128141, 135072, 142029, 148933, 155805, 162662, 169511, 176302, 183072, 189880, 196645, 203362, 210109, 216816, 223492, 230209

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038815, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^5 ], {n, 1, 30}]
```

a(n)=primepi(10^5*n) \\ Charles R Greathouse IV, Apr 29 2015

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

A038815 Number of primes less than n*10^6.

Original entry on oeis.org

78498, 148933, 216816, 283146, 348513, 412849, 476648, 539777, 602489, 664579, 726517, 788060, 849252, 910077, 970704, 1031130, 1091314, 1151367, 1211050, 1270607, 1329943, 1389261, 1448221, 1507122, 1565927, 1624527, 1683065

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038816, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^6 ], {n, 1, 30}]
```

a(n)=primepi(10^6*n) \\ Charles R Greathouse IV, Apr 29 2015

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

A038816 Number of primes less than n*10^7.

Original entry on oeis.org

664579, 1270607, 1857859, 2433654, 3001134, 3562115, 4118064, 4669382, 5216954, 5761455, 6303309, 6841648, 7378187, 7912199, 8444396, 8974458, 9503083, 10030385, 10555473, 11078937, 11601626, 12122540, 12642573

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038815, A038817, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^7 ], {n, 1, 30} ]
```

a(n)=primepi(10^7*n) \\ Charles R Greathouse IV, Apr 29 2015

More terms from Robert G. Wilson v, Aug 27 2001

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

A038817 Number of primes less than n*10^8.

Original entry on oeis.org

5761455, 11078937, 16252325, 21336326, 26355867, 31324703, 36252931, 41146179, 46009215, 50847534, 55662470, 60454705, 65228333, 69985473, 74726528, 79451833, 84163019, 88862422, 93547928, 98222287, 102886526, 107540122

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038815, A038816, A038818, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^8 ], {n, 1, 22}]
```

a(n)=primepi(10^8*n) \\ Charles R Greathouse IV, Apr 29 2015

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

A038818 Number of primes less than n*10^9.

Original entry on oeis.org

50847534, 98222287, 144449537, 189961812, 234954223, 279545368, 323804352, 367783654, 411523195, 455052511, 498388617, 541555851, 584570200, 627440336, 670180516, 712799821, 755305935, 797703398, 840000027, 882206716, 924324489

Offset: 1

Jeff Burch

nonn

Robert G. Wilson v, Table of n, a(n) for n = 1..10000
Andrew R. Booker, The Nth Prime Page
Thomas R. Nicely, Some Results of Computational Research in Prime Numbers [See local copy in A007053]
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A038801, A028505, A038812, A038813, A038814, A038815, A038816, A038817, A038819, A038820, A038821, A080122, A080123, A080124, A080125, A080126, A080127, A080128, A080129.

Mathematica
```
Table[ PrimePi[ n*10^9 ], {n, 1, 22}]
```

a(n)=primepi(10^9*n) \\ Charles R Greathouse IV, Apr 29 2015

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

cp's OEIS Frontend

A038811 Duplicate of A028505.

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A038822 Number of primes between 100n and 100n+99.

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A038801 Number of primes less than 10n.

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A038812 Number of primes less than 1000n.

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A038813 Number of primes less than 10000n.

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A038814 Number of primes less than 100000n.

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A038815 Number of primes less than n*10^6.

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A038816 Number of primes less than n*10^7.

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Mathematica