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.

Previous Showing 11-17 of 17 results.

A045523 Numbers k such that k! has initial digit '4'.

Original entry on oeis.org

8, 12, 26, 53, 57, 73, 82, 118, 129, 155, 160, 169, 185, 212, 215, 218, 232, 240, 265, 272, 281, 294, 338, 351, 369, 376, 388, 393, 398, 403, 408, 421, 432, 443, 446, 482, 485, 498, 515, 522, 533, 544, 548, 576, 580, 593, 602, 616, 621, 641, 646, 657, 668
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

The asymptotic density of this sequence is log_10(5/4) = 0.096910... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			8 is a term since 8! = 40320 has the initial digit 4.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A008905.

Programs

  • Mathematica
    Select[ Range[ 700 ], IntegerDigits[ #! ] [[ 1 ]] == 4 & ]
  • PARI
    isok(n) = digits(n!)[1] == 4; \\ Michel Marcus, Feb 07 2017

Formula

A008905(a(n)) = 4. - Amiram Eldar, Jul 17 2020

A045524 Numbers k such that k! has initial digit '5'.

Original entry on oeis.org

7, 21, 38, 46, 61, 66, 81, 119, 137, 144, 150, 165, 189, 196, 206, 209, 221, 224, 235, 243, 248, 253, 258, 279, 292, 340, 342, 353, 362, 383, 413, 429, 440, 488, 508, 529, 540, 584, 597, 611, 630, 651, 662, 679, 685, 704, 711, 718, 725, 732, 764, 782, 812
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

n such that A000030(A000142(n)) = 5. - Robert Israel, Feb 07 2017
The asymptotic density of this sequence is log_10(6/5) = 0.079181... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			7 is a term since 7! = 5040 has the initial digit 5.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045525, A045526, A045527, A045528, A045529.
Cf. A000030, A000142, A008905.

Programs

  • Maple
    filter:= proc(t) local tf;
tf:= t!;
floor(tf/10^ilog10(tf)) = 5
end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 07 2017
  • Mathematica
    Select[ Range[ 850 ], IntegerDigits[ #! ] [[1]] == 5 & ]
  • PARI
    isok(n) = digits(n!)[1] == 5; \\ Michel Marcus, Feb 08 2017

Formula

A008905(a(n)) = 5. - Amiram Eldar, Jul 17 2020

A045525 Numbers k such that k! has initial digit '6'.

Original entry on oeis.org

3, 13, 18, 24, 43, 49, 72, 120, 130, 138, 174, 178, 182, 193, 203, 227, 263, 270, 290, 309, 311, 313, 315, 317, 319, 321, 355, 364, 371, 378, 390, 395, 400, 405, 418, 426, 437, 457, 460, 463, 466, 469, 491, 501, 511, 518, 525, 536, 555, 559, 563, 567, 571
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

The asymptotic density of this sequence is log_10(7/6) = 0.066946... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			3 is a term since 3! = 6 has the initial digit 6.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A008905.

Programs

  • Mathematica
    Select[ Range[ 600 ], IntegerDigits[ #! ] [ [1] ] == 6 & ]
  • PARI
    isok(n) = digits(n!)[1] == 6; \\ Michel Marcus, Feb 08 2017

Formula

A008905(a(n)) = 6. - Amiram Eldar, Jul 17 2020

A045526 Numbers k such that k! has initial digit '7'.

Original entry on oeis.org

6, 56, 80, 156, 161, 170, 186, 200, 230, 238, 277, 288, 305, 307, 323, 325, 327, 344, 385, 410, 451, 454, 472, 475, 504, 532, 547, 551, 575, 592, 601, 615, 645, 661, 697, 710, 724, 731, 790, 800, 811, 822, 848
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

The asymptotic density of this sequence is log_10(8/7) = 0.057991... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			6 is a term since 6! = 720 has the initial digit 7.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A008905.

Programs

  • Mathematica
    Select[ Range[ 900 ], IntegerDigits[ #! ] [[1]] == 7 & ]
  • PARI
    isok(n) = digits(n!)[1] == 7; \\ Michel Marcus, Feb 08 2017

Formula

A008905(a(n)) = 7. - Amiram Eldar, Jul 17 2020

A045527 Numbers k such that k! has initial digit '8'.

Original entry on oeis.org

14, 29, 31, 33, 40, 52, 60, 65, 71, 79, 121, 131, 145, 151, 246, 251, 256, 286, 303, 329, 346, 357, 373, 423, 434, 448, 478, 494, 543, 579, 610, 650, 678, 684, 703, 738, 746, 754, 771, 780, 810, 834, 847
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

The asymptotic density of this sequence is log_10(9/8) = 0.051152... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			14 is a term since 14! = 87178291200 has the initial digit 8.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A008905.

Programs

  • Mathematica
    Select[ Range[ 900 ], IntegerDigits[ #! ] [ [1] ] == 8 & ]
  • PARI
    isok(n) = digits(n!)[1] == 8; \\ Michel Marcus, Feb 08 2017

Formula

A008905(a(n)) = 8. - Amiram Eldar, Jul 17 2020

A045528 Numbers k such that k! has initial digit '9'.

Original entry on oeis.org

96, 97, 98, 99, 100, 101, 102, 103, 122, 139, 166, 190, 233, 241, 261, 268, 301, 331, 366, 380, 415, 431, 445, 481, 497, 514, 521, 583, 596, 624, 629, 634, 655, 672, 690, 716, 723, 762, 789, 799, 821, 833, 861, 897
Offset: 1

Views

Author

Jeff Burch

Keywords

Comments

The asymptotic density of this sequence is log_10(10/9) = 1 - log_10(9) = 0.045757... (A104140) (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			96 is a term since 96! = 9.916779... * 10^149 has the initial digit 9.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A008905, A104140.

Programs

  • Mathematica
    Select[ Range[ 900 ], IntegerDigits[ #! ] [ [1] ] == 9 & ]
  • PARI
    isok(n) = digits(n!)[1] == 9; \\ Michel Marcus, Feb 08 2017

Formula

A008905(a(n)) = 9. - Amiram Eldar, Jul 17 2020

Extensions

More terms from Robert G. Wilson v, Jan 03 2001

A282021 Factorials with initial digit '7'.

Original entry on oeis.org

720, 710998587804863451854045647463724949736497978881168458687447040000000000000, 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000
Offset: 1

Views

Author

N. J. A. Sloane, Feb 07 2017

Keywords

Comments

Benford's law shows that this sequence will contain about (log(8) - log(7))/log(10) =~ 5.8% of all factorials.

Links

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142.

Programs

  • Mathematica
    Select[Range[100]!, First[IntegerDigits[#]] == 7 &] (* Vincenzo Librandi, Feb 08 2017 *)

Formula

a(n) = A000142(A045526(n)). - Amiram Eldar, Jul 19 2020
Previous Showing 11-17 of 17 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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