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.

Showing 1-10 of 12 results. Next

A119290 a(n) is the total number of digits in the first 10^n primes.

Original entry on oeis.org

1, 16, 271, 3803, 48982, 610484, 7245905, 83484450, 942636916, 10487584405, 115369529592, 1257761617574, 13611696080735, 146406754329933, 1566562183907264, 16687323842873339, 177063766685219106, 1872323812397478246, 19738266145121133639, 207517446542560214799, 2176390177056541482871, 22774922890367225576581
Offset: 0

Views

Author

Enoch Haga, May 13 2006

Keywords

Examples

			At a(1) there are 10^1 primes, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and the total number of digits is 16.
		

Crossrefs

Programs

  • Mathematica
    Accumulate@Table[c = 0; i0 = If[n == 0, 1, 10^(n - 1) + 1]; For[i = i0, i <= 10^n, i++, c += IntegerLength[Prime[i]]]; c, {n, 0, 6}] (* Robert Price, Jun 09 2019 *)

Formula

Count the digits in the first 10^n primes.
a(n) = sum while positive from k=0 to (10^n - A006880(k)). - Charles R Greathouse IV, Jul 09 2007

Extensions

Corrected and extended by Charles R Greathouse IV, Jul 09 2007

A228413 Count of the first 10^n primes which do not contain the digit 1.

Original entry on oeis.org

1, 6, 54, 532, 4675, 34425, 262549, 2051466, 16831152, 155616459, 1529462564, 14830618421, 141585123501
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(2) = 54 since there are 54 primes less than 541 (the 100th prime) that do not contain a 1.  Namely: 2, 3, 5, 7, 23, 29, ..., 523.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 1] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A228421 Count of the first 10^n primes which do not contain the digit 9.

Original entry on oeis.org

1, 8, 69, 620, 5010, 45732, 418142, 3785060, 32579606, 296601070, 2683254222, 24354108057, 212324183352
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(1) = 8 since there are 8 primes in the first 10 (through 29) that do not contain a 9.  Namely: 2, 3, 5, 7, 11, 13, 17, 23.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 9] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)
  • Python
    def a(n):
        count = 0
        for k in range(1,10**n+1):
            if '9' not in str(prime(k)):
                count += 1
        return count
    n = 0
    while n < 10:
        print(a(n), end=', ')
        n += 1
    # Derek Orr, Jul 27 2014

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A231412 Count of the first 10^n primes which do not contain the digit 0.

Original entry on oeis.org

1, 10, 91, 819, 7122, 61702, 557224, 5062320, 45002763, 395879190, 3579400605, 32487367715, 294505958253
Offset: 0

Views

Author

Robert Price, Nov 08 2013

Keywords

Examples

			a(2) = 91 = 100-9 since only 9 primes less than 541 (the 100th prime) contain a zero.  Namely: 101, 103, 107, 109, 307, 401, 409, 503, 509.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 0] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A183196 Total number of digits in the numbers involved in generating A183194.

Original entry on oeis.org

16, 36, 36, 97, 97, 97, 6314, 24404, 24404, 180346, 871640, 871640, 1817221, 3893939, 3893939, 79665948, 1046312296, 1046312296, 1046312296, 1046312296, 1046312296, 4754824913842, 6377067475119, 6377067475119
Offset: 1

Views

Author

James G. Merickel, Dec 31 2010

Keywords

Examples

			a(2)=36 since A019518(2)=20 and A183195(20)=235...616771 has 36 digits.
		

Crossrefs

Formula

a(n) = A055642(A183195(A019518(n))).

A228414 Count of the first 10^n primes which do not contain the digit 2.

Original entry on oeis.org

0, 7, 77, 697, 6497, 55552, 512100, 4710641, 42205969, 341224891, 2787791578, 22971326749, 190650687957
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(1) = 7 since there are 7 primes less than 29 (the 10th prime) that do not contain a 2.  Namely: 3, 5, 7, 11, 13, 17, 19.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 2] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) < 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A228415 Count of the first 10^n primes which do not contain the digit 3.

Original entry on oeis.org

1, 7, 54, 534, 4909, 45405, 385008, 3539880, 32260781, 294001190, 2564080248, 23271246324, 211753431947
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(1) = 7 since there are 7 primes in the first 10 (through 29) that do not contain a 3.  Namely: 2, 5, 7, 11, 17, 19, 29.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 3] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A228416 Count of the first 10^n primes which do not contain the digit 4.

Original entry on oeis.org

1, 10, 75, 721, 6637, 60605, 514809, 4730382, 43254591, 392344689, 3421561753, 31049600245, 282499317912
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(1) = 10 since there are 10 primes in the first 10 (through 29) that do not contain a 4.  Namely: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 4] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A228417 Count of the first 10^n primes which do not contain the digit 5.

Original entry on oeis.org

1, 9, 85, 708, 6635, 60640, 535534, 4737129, 43297195, 392641522, 3536880527, 31067514571, 282635824867
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(1) = 9 since there are 9 primes in the first 10 (through 29) that do not contain a 5.  Namely: 2, 3, 7, 11, 13, 17, 19, 23, 29.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 5] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024

A228418 Count of the first 10^n primes which do not contain the digit 6.

Original entry on oeis.org

1, 10, 90, 719, 6696, 60845, 554933, 4742037, 43331008, 392875212, 3573268469, 31207451849, 282765603085
Offset: 0

Views

Author

Robert Price, Nov 09 2013

Keywords

Examples

			a(1) = 10 since there are 10 primes in the first 10 (through 29) that do not contain a 6.  Namely: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
		

Crossrefs

Programs

  • Mathematica
    Table[Length[Select[Range[10^n], DigitCount[Prime[#], 10, 6] == 0 &]], {n, 0, 5}] (* Robert Price, Mar 23 2020 *)

Formula

a(n) <= 9^n. - Charles R Greathouse IV, May 21 2014

Extensions

a(12) from Lucas A. Brown, Mar 19 2024
Showing 1-10 of 12 results. Next