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

A217398 Numbers starting with 5.

Original entry on oeis.org

5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542
Offset: 1

Views

Author

Jeremy Gardiner, Oct 02 2012

Keywords

Comments

The lower and upper asymptotic densities of this sequence are 1/45 and 5/27, respectively. - Amiram Eldar, Feb 27 2021
Also numbers such that when the leftmost digit is moved to the unit's place the result is divisible by 5. - Stefano Spezia, Jul 08 2025

Links

Crossrefs

Cf. A000867, A011535.
Subsequences include: A045711, A077330, A077681, A106415, A106425.
Cf. A131835, A217394, A217395, A217397, A217399, A217400, A217401, A217402.

Programs

  • Haskell
    a217398 n = a217398_list !! (n-1)
a217398_list = filter ((== 5) . a000030) [1..]
-- Reinhard Zumkeller, Mar 13 2014
  • Mathematica
    Select[Range[1000], IntegerDigits[#][[1]] == 5 &] (* T. D. Noe, Oct 02 2012 *)
  • Python
    def A217398(n): return n+(44*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

A000030(a(n)) = 5; A143473(a(n)) = a(n). - Reinhard Zumkeller, Mar 13 2014
a(n) = n + (44*10^floor(log_10(9*n-8))-8)/9. - Alan Michael Gómez Calderón, May 17 2023

A077327 Smallest number beginning with 2 and having exactly n distinct prime divisors.

Original entry on oeis.org

2, 20, 204, 210, 2310, 200970, 2012010, 20030010, 223092870, 20090100030, 200560490130, 20055767721990, 2000029432190790, 20384767656323070, 2000848249650860610, 200001648981983238390, 2183473617971732996910
Offset: 1

Views

Author

Amarnath Murthy, Nov 04 2002

Keywords

Examples

			a(1) = 2, a(5) = 2310 = 2*3*5*7*11.

Crossrefs

Cf. A077326, A077328, A077329, A077330, A077331, A077332, A077333, A077334.
Cf. A106411-A106419, A106421-A106429.

Programs

  • Python
    from sympy import primorial, factorint
def a(n, begins_with=2): # use begins_with 1-9 for A077326-A077334
  m, start_digit = primorial(n), str(begins_with)
  while len(factorint(m)) != n or str(m)[0] != start_digit:
    m += 1
    s = str(m)
    if s[0] == start_digit: continue
    elif s[0] < start_digit: m = int(start_digit+'0'*(len(s)-1))
    else: m = int(start_digit+'0'*len(s))
  return m
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Feb 20 2021

Extensions

Correct a(2) and a(3), add a(6)-a(11) from Ray Chandler, Apr 17 2005
More terms from Ray Chandler, May 02 2005

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

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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