A261470 -id:A261470 - cp's OEIS frontend

A022885 Primes p=prime(k) such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

5, 7, 11, 13, 23, 37, 53, 73, 97, 101, 103, 109, 137, 157, 179, 191, 223, 251, 263, 307, 353, 373, 389, 409, 419, 433, 457, 479, 487, 541, 563, 571, 593, 683, 691, 701, 757, 809, 821, 853, 859, 877, 883, 911, 977, 1019, 1039, 1049, 1087, 1103

Offset: 1

Clark Kimberling

nonn

These are primes p for which the subsequent alternate prime gaps are equal, so (p(k+3)-p(k+2))/(p(k+1)-p(k)) = 1. It is conjectured that the most frequent alternate prime gaps ratio is one. - Andres Cicuttin, Nov 07 2016

			Starting from 5, the four consecutive primes are 5, 7, 11, 13; and they satisfy 5 + 13 = 7 + 11. So 5 is in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 Vincenzo Librandi)

Cf. A022884, A260179, A261470.

[NthPrime(n): n in [1..200] | (NthPrime(n)+NthPrime(n+3)) eq (NthPrime(n+1)+NthPrime(n+2))]; // Vincenzo Librandi, Nov 08 2016

Transpose[Select[Partition[Prime[Range[500]],4,1],First[#]+Last[#] == #[[2]]+#[[3]]&]][[1]] (* Harvey P. Dale, May 23 2011 *)

isok(p) = {my(k = primepi(p)); (p == prime(k)) && ((prime(k) + prime(k+3)) == (prime(k+1) + prime(k+2)));} \\ Michel Marcus, Jan 15 2014

from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    p, q, r, s = [2, 3, 5, 7]
    while True:
        if p + s == q + r: yield p
        p, q, r, s = q, r, s, nextprime(s)
print(list(islice(agen(), 50))) # Michael S. Branicky, May 31 2024

a(n) = A000040(A022884(n)). - Amiram Eldar, May 06 2020

Name edited by Michel Marcus, Jan 15 2014

A022884 Numbers k such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

Original entry on oeis.org

3, 4, 5, 6, 9, 12, 16, 21, 25, 26, 27, 29, 33, 37, 41, 43, 48, 54, 56, 63, 71, 74, 77, 80, 81, 84, 88, 92, 93, 100, 103, 105, 108, 124, 125, 126, 134, 140, 142, 147, 149, 151, 153, 156, 165, 171, 175, 176, 181, 185, 191, 200, 208, 211, 216, 224, 234, 235

Offset: 1

Clark Kimberling

nonn

			The ninth prime is 23. We verify that 23 + 37 = 60 = 29 + 31. Hence 9 is in the sequence.
The tenth prime is 29. We see that 29 + 41 = 70 but 31 + 37 = 68, so 10 is not in the sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Cf. A000720, A022885

Cf. A261470. - Altug Alkan, Oct 28 2015

[n: n in [1..250] |(NthPrime(n)+NthPrime(n+3)) eq (NthPrime(n+1)+ NthPrime(n+2))]; // Vincenzo Librandi, Nov 04 2018

Select[Range@ 240, Prime[#] + Prime[# + 3] == Prime[# + 1] + Prime[# + 2] &] (* Michael De Vlieger, Oct 28 2015 *)

isok(k) = prime(k+3)+prime(k) == prime(k+1)+prime(k+2); \\ Michel Marcus, Aug 20 2015

is(n,p=prime(n))=my(q=nextprime(p+1),r=nextprime(q+1),s=nextprime(r+1)); p+s==q+r
n=0; forprime(p=2,1e5, if(is(n++,p), print1(n", "))) \\ Charles R Greathouse IV, Oct 28 2015

a(n) = A000720(A022885(n)). - Zak Seidov, Oct 23 2015

Name edited by Michel Marcus, Aug 20 2015

cp's OEIS Frontend

A022885 Primes p=prime(k) such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

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A022884 Numbers k such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

Formula

Extensions