Luc Comeau-Montasse - cp's OEIS frontend

A214095 Position of integer n in the list of first n natural numbers written out in French and arranged in alphabetical order.

1, 1, 2, 2, 1, 4, 4, 3, 4, 3, 6, 4, 11, 8, 10, 11, 4, 4, 5, 20, 21, 21, 23

Offset: 1

Luc Comeau-Montasse, Jul 03 2012

			We have a(14) = 8 because of the ordered list: cinq, deux, dix, douze, huit, neuf, onze, quatorze, quatre, sept, six, treize, trois, un.

CF. A108017 (in English).

lista() = {my(v = ["un", "deux", "trois", "quatre", "cinq", "six", "sept", "huit", "neuf", "dix", "onze", "douze", "treize", "quatorze", "quinze", "seize", "dix-sept", "dix-huit", "dix-neuf", "vingt"], vs); for (i=1, #v, vp = vector(i, k, v[k]); vs = vecsort(vp); for (k=1, #vp, if (vs[k] == v[i], print1(k, ", "); break);););} \\ Michel Marcus, Jan 03 2019

A210435 Number of digits in 5^n.

Original entry on oeis.org

1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47

Offset: 0

Luc Comeau-Montasse, Mar 21 2012

			a(4) = 3 because 5^4 = 625, which has 3 digits.
a(5) = 4 because 5^5 = 3125, which has 4 digits.

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Ana Rechtman, Octobre 2015, 3e Défi, Images des Mathématiques, CNRS, 2015 (in French).

Cf. A000351, A055642.

Number of digits in b^n: A034887 (b=2), A034888 (b=3), A210434 (b=4), A210435 (b=5), A210436 (b=6), A210062 (b=7).

[#Intseq(5^n): n in [0..67]]; // Bruno Berselli, Mar 22 2012

a:= n-> length(5^n): seq(a(n), n=0..100); # Alois P. Heinz, Mar 22 2012

Table[Length[IntegerDigits[5^n]], {n, 0, 67}] (* Bruno Berselli, Mar 22 2012 *)
IntegerLength[5^Range[0,70]] (* Harvey P. Dale, Mar 26 2013 *)

a(n) = #Str(5^n); \\ Michel Marcus, Oct 27 2015

a(n) = A055642(A000351(n)) = A055642(5^n) = floor(log_10(10*(5^n))). [Jonathan Vos Post, Mar 22 2012]

a(n) + A034887(n) = n+1. - Michel Marcus, Oct 27 2015

A210434 Number of digits in 4^n.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 41

Offset: 0

Luc Comeau-Montasse, Mar 21 2012

Since log10(4) = A114493 ~ 0.60205 (= twice log10(2) = 0.30102999566...), the first 98 terms are equal to floor(n*3/5)+1. - M. F. Hasler, Mar 31 2025

			a(4) = 3 because 4^4 = 256, which has 3 digits.
a(5) = 4 because 4^5 = 1024, which has 4 digits.

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000302, A034887, A034888, A210062, A210435, A210436.

[#Intseq(4^n): n in [0..68]]; // Bruno Berselli, Mar 22 2012

a:= n-> length(4^n): seq(a(n), n=0..100); # Alois P. Heinz, Mar 22 2012

Table[Length[IntegerDigits[4^n]], {n, 0, 68}] (* Bruno Berselli, Mar 22 2012 *)

apply( {A210434(n)=logint(4^n,10)+1}, [0..66]) \\ M. F. Hasler, Mar 31 2025

a(n)=log(4)*n\log(10)+1 \\ correct up to n ~ 10^precision, with default precision = 38. - M. F. Hasler, Mar 31 2025

from math import log
def A210434(n): return int(n*log(4,10))+1 if n<1e16 else "not enough precision" # M. F. Hasler, Mar 31 2025

a(n) = A055642(A000302(n)) = A055642(4^n) = floor(log_10(10*(4^n))). - Jonathan Vos Post, Mar 22 2012

A210436 Number of digits in 6^n.

Original entry on oeis.org

1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 15, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 35, 36, 36, 37, 38, 39, 39, 40, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 50, 50, 51, 52, 53

Offset: 0

Luc Comeau-Montasse, Mar 21 2012

			a(4) = 4 because 6^4 = 1296, which has 4 digits.
a(5) = 4 because 6^5 = 7776, which has 4 digits.

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000400, A034887, A034888, A210062, A210434, A210435.

[#Intseq(6^n): n in [0..67]]; // Bruno Berselli, Mar 22 2012

a:= n-> length(6^n): seq (a(n), n=0..100); # Alois P. Heinz, Mar 22 2012

Table[Length[IntegerDigits[6^n]], {n, 0, 99}] (* Alonso del Arte, Mar 22 2012 *)

a(n) = A055642(A000400(n)) = A055642(6^n) = floor(log_10(10*(6^n))). - Jonathan Vos Post, Mar 23 2012

A210062 Number of digits in 7^n.

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 33, 34, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 55, 56, 57

Offset: 0

Luc Comeau-Montasse, Mar 16 2012

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000420, A055642.

Number of digits in b^n: A034887 (b=2), A034888 (b=3), A210434 (b=4), A210435 (b=5), A210436 (b=6), this sequence (b=7).

[#Intseq(7^n): n in [0..67]]; // Bruno Berselli, Mar 22 2012

Table[Length[IntegerDigits[7^n]], {n, 0, 100}] (* T. D. Noe, Mar 20 2012 *)

a(n) = A055642(A000420(n)) = A055642(7^n) = floor(log_10(10*(7^n))). [Jonathan Vos Post, Mar 23 2012]

A166931 Numbers n with property that n mod k is k-1 for all k = 2..9.

Original entry on oeis.org

2519, 5039, 7559, 10079, 12599, 15119, 17639, 20159, 22679, 25199, 27719, 30239, 32759, 35279, 37799, 40319, 42839, 45359, 47879, 50399, 52919, 55439, 57959, 60479, 62999, 65519, 68039, 70559, 73079, 75599, 78119, 80639, 83159, 85679

Offset: 1

Luc Comeau-Montasse, Oct 23 2009

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2, -1).

isA166931 := proc(n) for k from 2 to 9 do if n mod k <> k-1 then return false; end if; end do; true; end proc: for n from 1 to 500000 do if isA166931(n) then printf("%d,",n) ; end if; end do ; # R. J. Mathar, Nov 02 2009

Select[Range[90000],And@@Table[Mod[#,k]==k-1,{k,2,9}]&] (* Harvey P. Dale, Jun 14 2011 *)
LinearRecurrence[{2, -1}, {2519, 5039}, 50] (* G. C. Greubel, May 28 2016 *)

a(n) = 2519 + n*2520.
From G. C. Greubel, May 28 2016: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (2519 + x)/(1-x)^2.
E.g.f.: (2519 + 2520*x)*exp(x). (End)

Edited by N. J. A. Sloane, Oct 25 2009

A144965 a(n) = 4n(4*n^2 + 1).

Original entry on oeis.org

0, 20, 136, 444, 1040, 2020, 3480, 5516, 8224, 11700, 16040, 21340, 27696, 35204, 43960, 54060, 65600, 78676, 93384, 109820, 128080, 148260, 170456, 194764, 221280, 250100, 281320, 315036, 351344, 390340, 432120, 476780, 524416, 575124, 629000, 686140, 746640

Offset: 0

Luc Comeau-Montasse, Sep 27 2008

(a(n))^2 + (n*a(n)+1)^2 is always a perfect square.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Luc Comeau-Montasse, Des mesures entières pour des triangles rectangles, Géométrie et nombre (French blog), September 2008.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A008586, A053755, A317297.

I:=[0, 20, 136, 444]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012

CoefficientList[Series[4*x*(5+14*x+5*x^2)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jun 30 2012 *)
LinearRecurrence[{4,-6,4,-1},{0,20,136,444},50] (* Harvey P. Dale, Aug 07 2022 *)

G.f.: 4*x*(5+14*x+5*x^2)/(1-x)^4. - Colin Barker, May 24 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 30 2012
From Elmo R. Oliveira, Aug 07 2025: (Start)
E.g.f.: 4*x*(5 + 2*x)*(1 + 2*x)*exp(x).
a(n) = 4*A317297(n+1) = A008586(n)*A053755(n). (End)

A131654 Difference mod 10 of successive digits of Pi.

Original entry on oeis.org

8, 3, 7, 4, 4, 3, 4, 9, 8, 2, 3, 1, 8, 2, 4, 9, 1, 5, 6, 2, 6, 4, 8, 9, 0, 5, 5, 9, 5, 2, 6, 5, 2, 6, 0, 6, 7, 8, 8, 4, 5, 3, 4, 6, 0, 4, 4, 8, 6, 9, 5, 3, 4, 8, 9, 8, 7, 5, 5, 0, 1, 4, 3, 1, 7, 7, 1, 3, 5, 8, 6, 6, 6, 6, 8, 6, 8, 8, 1, 0, 9, 8, 6, 6, 2, 3, 1, 4, 4, 3, 8, 1, 8, 9, 0, 6, 3, 6, 1, 2, 9, 4, 9, 3, 4

Offset: 0

Luc Comeau-Montasse, Sep 10 2007

Mod[Differences[RealDigits[Pi,10,120][[1]]],10] (* Harvey P. Dale, Jul 28 2021 *)

More terms from Robert G. Wilson v, Sep 14 2007

cp's OEIS Frontend

User: Luc Comeau-Montasse

A214095 Position of integer n in the list of first n natural numbers written out in French and arranged in alphabetical order.

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A210435 Number of digits in 5^n.

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A210434 Number of digits in 4^n.

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A210436 Number of digits in 6^n.

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A210062 Number of digits in 7^n.

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A166931 Numbers n with property that n mod k is k-1 for all k = 2..9.

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A144965 a(n) = 4*n*(4*n^2 + 1).

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A144965 a(n) = 4n(4*n^2 + 1).