A101432 -id:A101432 - cp's OEIS frontend

A000655 a(n) = number of letters in a(n-1), a(1) = 1 (in English).

1, 3, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

N. J. A. Sloane

Decimal expansion of 1219/900. - Elmo R. Oliveira, May 05 2024

			One, three, five, four, four, four, ...

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A005589 (number of letters).

Cf. A061504 (French), A101432 (Spanish), A328263 (Polish).

Nest[Append[#, StringLength@ IntegerName[#[[-1]], "Words"]] &, {1}, 105] (* Michael De Vlieger, Feb 17 2021 *)

a(n) = 4 for n > 3, with a(1) = 1, a(2) = 3 and a(3) = 5. - Wesley Ivan Hurt, Oct 03 2020
E.g.f.: - 4 - 3*x - (1/2)*x^2 + (1/6)*x^3 + 4*exp(x). - Alejandro J. Becerra Jr., Feb 17 2021
G.f.: x*(1+2*x+2*x^2-x^3)/(1-x). - Elmo R. Oliveira, Jun 25 2024

A328263 a(n) = number of letters in a(n-1) (in Polish), with a(1) = 1.

Original entry on oeis.org

1, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6, 5, 4, 6

Offset: 1

Robert Bilinski, Oct 09 2019

a(1) = 1; for n>1, a(n) = numbers of letters in Polish name for a(n-1).

Decimal expansion of 515/333. - Elmo R. Oliveira, May 05 2024

			Jeden, pięć, cztery, sześć, pięć, ...

Robert Bilinski, Table of n, a(n) for n = 1..99
Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Cf. A008962 (number of letters).

Cf. A000655 (English), A061504 (French), A101432 (Spanish).

a(n) = a(n-3) for n > 4. - Elmo R. Oliveira, May 05 2024

A061504 a(1) = 1; for n>1, a(n) = numbers of letters in French name for a(n-1).

Original entry on oeis.org

1, 2, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4, 6, 3, 5, 4

Offset: 1

N. J. A. Sloane, Jun 14 2001

a(n+1) = le nombre des lettres dans a(n), a(1) = 1 (in French).
The English (1, 3, 5, 4, 4, 4, ...) and German (1, 4, 4, 4, ...) versions are less interesting.
Decimal expansion of 13847/11110 = 1.24635463546354635... - Eric Angelini, Sep 17 2006; corrected by Elmo R. Oliveira, Jun 29 2024

			Un, deux, quatre, six, trois, cinq, quatre, ...
UN (2 letters), DEUX (4 letters), QUATRE (6 letters), SIX (3 letters), TROIS (5 letters), CINQ (4 letters), QUATRE (6 letters), ...

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A007005 (number of letters).

Cf. A000655 (English), A101432 (Spanish), A328263 (Polish).

From Elmo R. Oliveira, Jun 29 2024: (Start)
G.f.: x*(1+2*x+4*x^2+6*x^3+2*x^4+3*x^5)/(1-x^4).
a(n) = a(n-4) for n > 6. (End)

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007

A226294 Period 2: repeat [6, 4].

Original entry on oeis.org

6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6

Offset: 0

Richard R. Forberg, Jun 02 2013

A two number repeating sequence for constructing a summation sequence from negative to positive infinity containing all primes except 2 and 5.
Essentially the same as A168428, A101432 and A010711.
NOTE: This sequence has a shift in the starting value at index 0 relative to A010711. It is used here for the purpose stated with positive and negative indices making the formula in A010711 non-applicable.
This infinitely repeating sequence, a(n), of two numbers (6,4) starting with a(0) = 6, allows for the creation of an infinite summation sequence, s(n), extending from negative to positive infinity, using the formula below in parallel with how the same is done in A226276 using a different repeating sequence. Letting "s(n+)" be the set positive s(n) values, and "s(n-)" be the absolute value of the set of negative s(n) values, the following applies:
s(n+) includes all numbers with last digits of 1 and 7.
s(n-) includes all numbers with last digits of 3 and 9.
Therefore, s(n) includes all primes (except 2 and 5) without duplication.
This is one of only two such repeating patterns that accomplish this goal relative to the primes, while excluding all numbers with a last digit of 5. The other is (8,4,4,4) but with a different split between which primes occur as positive vs. negative numbers. See A226276 for details. Both patterns have the same density of primes relative to all s(n), and both, presumably, have the same average density of primes as positive vs. negative values of s(n).

			s(1) = 7, s(2) = 11, s(3) = 17, s(4) = 21, s(5) = 27, s(6) = 31;
s(-1) = -3, s(-2) = -9, s(-3) = -13, s(-4) = -19, s(-5) = -23, s(-6) = -29;

Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010711, A101432, A168428, A226276.

&cat [[6, 4]^^50]; // Wesley Ivan Hurt, Jul 18 2016

A226294:=n->5+(-1)^n: seq(A226294(n), n=0..100); # Wesley Ivan Hurt, Mar 24 2014

Table[5+(-1)^n, {n,0,100}] (* Wesley Ivan Hurt, Mar 24 2014 *)

a(n)=6-n%2*2 \\ Charles R Greathouse IV, Jul 17 2016

a(n) = 5+(-1)^n = 2*A176059(n).
To generate the summation sequence s(n), start with s(0) = 1, and a(0) = 6.
For positive values of s(n):  s(n+1) = s(n) + a(n)
For negative values of s(n):  s(n-1) = s(n) - a(n-1). n is negative here.
See example values for s(n) below, for both positive and negative indices.
G.f.: ( 6+4*x ) / ( (1-x)*(1+x) ). - R. J. Mathar, Jun 12 2013
a(n) = a(n-2) for n>1. - Wesley Ivan Hurt, Jul 18 2016

cp's OEIS Frontend

A000655 a(n) = number of letters in a(n-1), a(1) = 1 (in English).

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A328263 a(n) = number of letters in a(n-1) (in Polish), with a(1) = 1.

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A061504 a(1) = 1; for n>1, a(n) = numbers of letters in French name for a(n-1).

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A226294 Period 2: repeat [6, 4].

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