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.

User: Jacques ALARDET

Jacques ALARDET's wiki page.

Jacques ALARDET has authored 12 sequences. Here are the ten most recent ones:

A234666 Number of combinations for the sum of 6 different numbers from 1 to 49.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 110, 136, 163, 199, 235, 282, 331, 391, 454, 532, 612, 709, 811, 931, 1057, 1206, 1360, 1540, 1729, 1945, 2172, 2432, 2702, 3009, 3331, 3692, 4070, 4494, 4935, 5426, 5940, 6506, 7097, 7748, 8423
Offset: 21

Views

Author

Jacques ALARDET, Dec 29 2013

Keywords

Examples

			a(21)=1 because the only way to sum to 21 is 1+2+3+4+5+6=21; a(279)=1 because 279 occurs only as 49+48+47+46+45+44.

Links

Crossrefs

A026812 contains the same values until A026812(49)=4935.

A203623 Partial sums of A061395.

Original entry on oeis.org

0, 1, 3, 4, 7, 9, 13, 14, 16, 19, 24, 26, 32, 36, 39, 40, 47, 49, 57, 60, 64, 69, 78, 80, 83, 89, 91, 95, 105, 108, 119, 120, 125, 132, 136, 138, 150, 158, 164, 167, 180, 184, 198, 203, 206, 215, 230, 232, 236, 239, 246, 252, 268, 270, 275, 279, 287
Offset: 1

Views

Author

Jacques ALARDET, Jan 04 2012

Keywords

Examples

			a(10) = a(9) + A061395(10) ; a(9)=16 ; A061395(10)=3 ;
a(10) = 16+3 = 19.

Formula

a(n) = a(n-1) + A061395(n)

A202358 Sum of digits of n^(n!).

Original entry on oeis.org

0, 1, 4, 18, 73, 334, 2592, 18919, 164476, 1558521, 1, 187044031, 2326111614, 31214008090
Offset: 0

Views

Author

Jacques ALARDET, Dec 17 2011

Keywords

Comments

a(10^k) = 1. - Chai Wah Wu, Dec 18 2019

Examples

			a(3) = 18 because 3^3! = 729 with digit sum 7+2+9 = 18.

Crossrefs

Cf. A053986, A007953, A202336.

Programs

  • Maple
    ds:= proc(n) local r;
       `if`(n<10, n, ds(iquo(n, 10^iquo(length(n), 2), 'r'))+ds(r))
     end:
a:= n-> ds(n^n!):
seq(a(n), n=0..10);  # Alois P. Heinz, Dec 17 2011
  • Python
    from math import factorial
def a(n): return sum(map(int, str(n**(factorial(n)))))
print([a(n) for n in range(10)]) # Michael S. Branicky, Jan 28 2021

Formula

a(n) = A007953(A053986(n)). - Michel Marcus, Aug 22 2013

Extensions

a(11)-a(12) from Lars Blomberg, Jan 18 2013
a(13) from Chai Wah Wu, Oct 25 2021

A202336 Number of digits in n^(n!).

Original entry on oeis.org

1, 1, 1, 3, 15, 84, 561, 4260, 36413, 346276, 3628801, 41569064, 516929544, 6936548425, 99917483647, 1537944393896, 25193549397053, 437655212248536, 8036723680196724, 155554110186062367, 3165278489148945082, 67553429525569109411, 1508884070229326953381
Offset: 0

Views

Author

Jacques ALARDET, Dec 17 2011

Keywords

Examples

			a(3) = 3 because 3^3! = 729 with 3 digits;
a(4) = 15 because 4^4! = 281474976710656 with 15 digits.

Links

Crossrefs

Cf. A053986, A202358.

Programs

  • Maple
    a:= proc(n) local h;
      Digits:= 1000;
      1+ `if`(n=0, 0, floor(n!*simplify(log[10](n))))
    end:
seq(a(n), n=0..30); # Alois P. Heinz, Dec 17 2011
  • Mathematica
    Table[IntegerLength[n^n!],{n,0,10}] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Nov 19 2024 *)

Formula

a(n) = A055642(A053986(n)). - Michel Marcus, Aug 22 2013

Extensions

More terms from Alois P. Heinz, Dec 17 2011

A202148 Sum of rows of the triangle in A080381.

Original entry on oeis.org

1, 2, 4, 8, 12, 32, 36, 100, 132, 392, 384, 1168, 1500, 5332, 5284, 15740, 16804, 60896, 62872, 222948, 243780, 927176, 876004, 2999432, 3284180, 12706832, 12636656, 45043700, 46679920, 176783132, 177597976, 652158968, 700632804, 2696835032, 2735898216
Offset: 0

Views

Author

Jacques ALARDET, Dec 12 2011

Keywords

Examples

			a(0)= 1.
a(4)= 1 + 2 + 6 + 2 + 1 = 12.

Crossrefs

Cf. A080381.

Programs

  • Mathematica
    Table[Total[Table[GCD[Binomial[n, j], Binomial[n, Floor[n/2]]], {j, 0, n}]], {n, 0, 50}]

A175042 Number of iterations required for A169639 to reach a loop.

Original entry on oeis.org

12, 11, 7, 12, 29, 17, 19, 20, 4, 17, 7, 20, 27, 29, 25, 24, 12, 5, 21, 29, 17, 17, 32, 28, 27, 10, 5, 17, 6, 30, 29, 6, 5, 18, 21, 10, 9, 6, 9, 26, 5, 9, 9, 16, 2, 9, 16, 9, 12, 25, 6, 21, 18, 15, 6, 6, 21, 21, 3, 17, 19, 8, 8, 13, 11, 17, 27, 8, 27, 28, 28, 26, 16, 23, 17, 5, 5, 17, 18
Offset: 1

Views

Author

Jacques ALARDET, Apr 05 2010

Keywords

Extensions

Edited by N. J. A. Sloane, Apr 05 2010

A175043 Apply the map n -> A169639(n) until a member of A169641 is obtained; sequence gives this member.

Original entry on oeis.org

247, 293, 177, 247, 293, 178, 178, 177, 177, 293, 286, 177, 246, 293, 236, 293, 247, 177, 246, 293, 178, 178, 246, 293, 293, 293, 177, 178, 177, 246, 293, 286, 232, 230, 236, 293, 293, 286, 177, 293, 177, 293, 293, 178, 232, 177, 293, 293, 247, 293, 177
Offset: 0

Views

Author

Jacques ALARDET, Apr 05 2010

Keywords

Examples

			0 ("zéro") => 64 ("soixante-quatre") => 189 ("cent quatre-vingt neuf") => 242 ("deux cent quarante-deux") => 247, which is in A169641.

Crossrefs

Cf. A169639, A169641, A167507.

A174984 Start with n, iterate the map k -> A167507(k) until we reach 3; a(n) = number of steps required.

Original entry on oeis.org

4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4, 4, 5, 4, 1, 3, 4, 2, 4, 4, 4
Offset: 1

Views

Author

Jacques ALARDET, Apr 03 2010

Keywords

Examples

			a(0): zero => 4 => quatre => 6 => six => 3 ==> length = 4. a(1): un => 2 => deux => 4 => quatre => 6 => six => 3 ==> length = 5.

Crossrefs

Cf. A167507, A174985.

Extensions

Edited by N. J. A. Sloane, Apr 05 2010

A174987 Start with n, iterate the map k -> A167507(k) until we reach 3, 4, 5 or 6; a(n) = which of 3, 4, 5 or 6 we reach first.

Original entry on oeis.org

4, 4, 4, 3, 4, 5, 6, 4, 4, 4, 3, 4, 5, 6, 4, 6, 5, 4, 4, 4, 5, 4, 4, 3, 4, 4, 4, 4, 4, 4, 6, 3, 3, 4, 5, 3, 4, 3, 3, 3, 4, 5, 5, 6, 4, 5, 4, 5, 5, 5, 4, 6, 6, 4, 6, 6, 5, 6, 6, 6, 4, 5, 5, 6, 4, 5, 4, 5, 5, 5, 4, 4, 6, 4, 5, 4, 6, 6, 6, 6, 5, 6, 6, 5, 4, 6, 4, 6, 6, 6, 4, 6, 5, 4, 4, 4, 5, 4, 4, 4
Offset: 1

Views

Author

Jacques ALARDET, Apr 03 2010

Keywords

Crossrefs

Cf. A167507, A174984, A174985.

Extensions

Edited by N. J. A. Sloane, Apr 05 2010

A174985 Start with n, iterate the map k -> A167507(k) until we reach 3, 4, 5 or 6; a(n) = number of steps required.

Original entry on oeis.org

2, 3, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 4, 4, 4, 3, 4, 4, 4
Offset: 1

Views

Author

Jacques ALARDET, Apr 03 2010

Keywords

Crossrefs

Cf. A167507, A174984, A174987.

Extensions

Edited by N. J. A. Sloane, Apr 05 2010

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

Content is available under The OEIS End-User License Agreement.