A133677 -id:A133677 - cp's OEIS frontend

A133645 Integers arising in A133677.

2, 5, 15, 77, 187, 345, 551, 1107, 1457, 1855, 2301, 3337, 4565, 5251, 6767, 7597, 8475, 11397, 12467, 14751, 18537, 19895, 21301, 24257, 25807, 34277, 36115, 38001, 41917, 43947, 46025, 48151, 52547, 57135, 64377, 66887, 80157, 82955, 85801

Offset: 1

Roger L. Bagula, Dec 28 2007

nonn

Robert Price, Table of n, a(n) for n = 1..10018

Union[Table[If[IntegerQ[Prime[n]*(2*Prime[n] - 1)/3], Prime[n]*(2*Prime[n] - 1)/3, {}], {n, 1, 100}]]

A091177 Numbers m such that the m-th prime is of the form 3*k-1.

Original entry on oeis.org

1, 3, 5, 7, 9, 10, 13, 15, 16, 17, 20, 23, 24, 26, 28, 30, 32, 33, 35, 39, 40, 41, 43, 45, 49, 51, 52, 54, 55, 56, 57, 60, 62, 64, 66, 69, 71, 72, 76, 77, 79, 81, 83, 86, 87, 89, 91, 92, 94, 96, 97, 98, 102, 103, 104, 107, 108, 109, 113, 116, 118, 119, 120, 123

Offset: 1

Ray Chandler, Dec 26 2003

A003627 indexed by A000040.

The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - Amiram Eldar, Feb 28 2021

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A003627 (primes of the form 3*k-1), A024893, A087370, A088879.

A133677 is another version.

PrimePi/@Select[3Range[0,250]-1,PrimeQ]  (* Harvey P. Dale, Apr 26 2011 *)
Select[Range[150],IntegerQ[(Prime[#]+1)/3]&] (* Harvey P. Dale, Dec 14 2021 *)

a091177(limit)={my(m=0);forprime(p=2,prime(limit),m++;if(p%3==2,print1(m,", ")))};
a091177(123) \\ Hugo Pfoertner, Aug 03 2021

a(n) = k such that A000040(k) = A003627(n).

A132194 a(n) = 1 if n-th prime is 0 or 2 mod 3, otherwise 0.

Original entry on oeis.org

1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0

Offset: 1

Roger L. Bagula, Nov 05 2007

Equivalently, a(n) = 0 if n-th prime is 1 mod 3, otherwise 1. - Wouter Meeussen, May 21 2019

Binary sequence based on the primes: play it at a slower tempo to appreciate the irregularities.

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for characteristic functions.

Characteristic function of A133677.

Cf. A039701, A130198, A099618.

[(NthPrime(n) mod 3) eq 1 select 0 else 1: n in [1..200]]; // G. C. Greubel, May 21 2019

a := n -> 1 - irem(modp(ithprime(n), 3), 2):
seq(a(n), n = 1..105); # Peter Luschny, May 21 2019

Table[If[Mod[Prime[n],3]== 1,0,1],{n,200}] (* Harvey P. Dale, May 21 2019 *)

{a(n) = if(prime(n)%3==1, 0, 1)}; \\ G. C. Greubel, May 21 2019

def a(n):
    if (mod(nth_prime(n), 3)==1): return 0
    else: return 1
[a(n) for n in (1..200)] # G. C. Greubel, May 21 2019

a(n) = 1-A099618(n). - R. J. Mathar, Jun 06 2019

Sum_{k=1..n} a(k) ~ n / 2. - Amiram Eldar, Mar 14 2025

Definition corrected by Harvey P. Dale, May 21 2019

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A133645 Integers arising in A133677.

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A091177 Numbers m such that the m-th prime is of the form 3*k-1.

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A132194 a(n) = 1 if n-th prime is 0 or 2 mod 3, otherwise 0.

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