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

A217399 Numbers starting with 6.

Original entry on oeis.org

6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642
Offset: 1

Views

Author

Jeremy Gardiner, Oct 02 2012

Keywords

Comments

The lower and upper asymptotic densities of this sequence are 1/54 and 10/63, respectively. - Amiram Eldar, Feb 27 2021

Links

Crossrefs

Cf. A000870, A011536.
Subsequences include: A045712, A077331, A077682, A106416, A106426.
Cf. A131835, A217394, A217395, A217397, A217398, A217400, A217401, A217402.

Programs

  • GAP
    Flat(List([0..2],n->List([0..10^n-1],k->6*10^n+k))); # Muniru A Asiru, Nov 21 2018
  • Magma
    [n: n in [1..1600] | Intseq(n)[#Intseq(n)] eq 6]; // Vincenzo Librandi, Nov 24 2018
  • Maple
    seq(seq(6*10^n+k, k=0..10^n-1),n=0..3); # Robert Israel, May 08 2017
  • Mathematica
    Select[Range[1000], IntegerDigits[#][[1]] == 6 &] (* T. D. Noe, Oct 02 2012 *)
  • PARI
    isok(n) = digits(n)[1] == 6; \\ Michel Marcus, May 08 2017
  • Python
    def A217399(n): return n+(53*10**(len(str(9*n-8))-1))//9 # Chai Wah Wu, Dec 07 2024

Formula

a(n) = n + (53*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

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

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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