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 1-9 of 9 results.

A077334 Smallest number beginning with 9 and having exactly n distinct prime divisors.

Original entry on oeis.org

9, 91, 90, 910, 9030, 90090, 903210, 9699690, 900029130, 9146807670, 901741380540, 9426343036110, 900781858106130, 90004386781078770, 914836017997511610, 90100977291211496610, 9000008798605567472730, 900002983747159323401370
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(2) = 91 = 13*7.

Crossrefs

Cf. A077326, A077327, A077328, A077329, A077330, A077331, A077332, A077333.
Cf. A106411-A106419, A106421-A106429.

Programs

  • PARI
    a(n) = {i = prod(i=1, n, prime(i)); while ((digits(i)[1] != 9) || (omega(i)!= n), i++); i;} \\ Michel Marcus, Sep 14 2013

Extensions

a(5)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A077326 Smallest number beginning with 1 and having exactly n distinct prime divisors.

Original entry on oeis.org

1, 11, 10, 102, 1020, 10010, 101010, 1009470, 11741730, 1001110110, 10407767370, 1000287585570, 10293281928930, 1001230315195110, 13082761331670030, 1004819888620217670, 100015003602410826930, 1922760350154212639070
Offset: 0

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Comments

What are the values of n where a(n) differ from A106411(n)? So far only n=4 is such a value. - Chai Wah Wu, May 07 2025

Examples

			a(0) = 1, a(5) = 10010 = 2*5*7*11*13.

Crossrefs

Cf. A077327, A077328, A077329, A077330, A077331, A077332, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

More terms from Sascha Kurz, Jan 04 2003
a(9)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A217394 Numbers starting with 2.

Original entry on oeis.org

2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242
Offset: 1

Views

Author

Jeremy Gardiner, Oct 02 2012

Keywords

Comments

The lower and upper asymptotic densities of this sequence are 1/18 and 10/27, respectively. - Amiram Eldar, Feb 27 2021

Links

Crossrefs

Cf. A006092, A011532.
Subsequences include: A045708, A045726, A077327, A077678, A106412, A106422.
Cf. A131835, A217395, A217397, A217398, A217399, A217400, A217401, A217402.

Programs

  • Mathematica
    Select[Range[300], IntegerDigits[#][[1]] == 2 &] (* T. D. Noe, Oct 02 2012 *)
  • Python
    def agen():
  yield 2
  digits, adder = 1, 20
  while True:
    for i in range(10**digits): yield adder + i
    digits, adder = digits+1, adder*10
g = agen()
print([next(g) for i in range(54)]) # Michael S. Branicky, Feb 20 2021
  • Python
    def A217394(n): return n+(17*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

a(n) = n + (17*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 15 2023

A077328 Smallest number beginning with 3 and having exactly n distinct prime divisors.

Original entry on oeis.org

3, 33, 30, 330, 3570, 30030, 3008460, 30120090, 300690390, 30043474230, 304075581810, 30035662366710, 304250263527210, 30078810535603830, 3001252188252588270, 32589158477190044730, 3003056284355533696290
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(1) = 3, a(6) = 30030 = 2*3*5*7*11*13.

Crossrefs

Cf. A077326, A077327, A077329, A077330, A077331, A077332, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

Correct a(3)=30 and add a(5)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A077329 Smallest number beginning with 4 and having exactly n distinct prime divisors.

Original entry on oeis.org

4, 40, 42, 420, 4290, 43890, 4001970, 40029990, 406816410, 40026056070, 401120980260, 40013061952710, 405332750552730, 40111962162442170, 4000228915204892370, 40909794684132183810, 4000669166940700163910
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(1) = 4, a(3) = 42.

Crossrefs

Cf. A077326, A077327, A077328, A077330, A077331, A077332, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

a(5)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A077330 Smallest number beginning with 5 and having exactly n distinct prime divisors.

Original entry on oeis.org

5, 50, 504, 510, 5460, 51870, 510510, 50169210, 504894390, 50007124860, 503520607590, 50000602191540, 501601785815130, 50073188107872930, 5000089945706645790, 50617203592231346070, 5000858931483646541310
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(4) = 510 = 2*3*5*17.

Crossrefs

Cf. A077326, A077327, A077328, A077329, A077331, A077332, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

More terms from Ray G. Opao, Aug 04 2004
a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A077331 Smallest number beginning with 6 and having exactly n distinct prime divisors.

Original entry on oeis.org

61, 6, 60, 630, 6006, 60060, 690690, 60090030, 601380780, 6469693230, 600319429710, 60007743265470, 600277546959090, 60039293728424010, 614889782588491410, 60865792091025932010, 6000526229622444289770, 600025752738409899231330
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(3) = 60 = 2^2*3*5.

Crossrefs

Cf. A077326, A077327, A077328, A077329, A077330, A077332, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

Corrected and extended by Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jul 21 2004
a(8)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A077332 Smallest number beginning with 7 and having exactly n distinct prime divisors.

Original entry on oeis.org

7, 72, 70, 714, 7140, 71610, 746130, 70136220, 703600590, 70015935990, 700288518930, 7420738134810, 701098433345310, 70007243563797540, 757887406446280110, 70025936403159126390, 7001749954335151685670, 700007496840185797172910
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(3) = 70 = 2*5*7.

Crossrefs

Cf. A077326, A077327, A077328, A077329, A077330, A077331, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

a(5)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

A077333 Smallest number beginning with 8 and having exactly n distinct prime divisors.

Original entry on oeis.org

8, 80, 84, 840, 8190, 81510, 870870, 80059980, 800509710, 8254436190, 800680310430, 8222980095330, 800160280950030, 80008785365579070, 843685980760953330, 80058789202898516010, 8001338333881400327820, 800009744613910196656290
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(3) = 84 = 2^2*3*7.

Crossrefs

Cf. A077326, A077327, A077328, A077329, A077330, A077331, A077332, A077334.
Cf. A106411-A106419, A106421-A106429.

Extensions

Corrected and extended by Sascha Kurz, Jan 30 2003
a(9)-a(10) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005
Showing 1-9 of 9 results.

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