A094343 -id:A094343 - cp's OEIS frontend

A140382 Duplicate of A094343.

3, 7, 7, 11, 13, 17, 19, 23, 37, 41, 43, 47, 67, 71, 79, 83, 97

Offset: 1

dead

A140446 List of prime pairs of form p, p+14.

3, 17, 5, 19, 17, 31, 23, 37, 29, 43, 47, 61, 53, 67, 59, 73, 83, 97, 89, 103, 113, 127, 137, 151, 149, 163, 167, 181, 179, 193, 197, 211, 227, 241, 257, 271, 263, 277, 269, 283, 293, 307, 317, 331, 353, 367, 359, 373, 383, 397, 419, 433, 443, 457, 449, 463

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

nonn

The two primes p and p+14 are not necessarily adjacent.

Is 17 the only term that appears twice? There are no other examples up to the 5 millionth prime. - Harvey P. Dale, Nov 14 2024

			The pairs are (3, 17), (5, 19), (17, 31) etc.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000040, A094343.

Flatten[{#,#+14}&/@Select[Prime[Range[100]],PrimeQ[#+14]&]] (* Harvey P. Dale, Nov 14 2024 *)

Corrected a(36) (241 with 271); more terms from Vincenzo Librandi, Oct 18 2009

A140447 List of prime pairs of form p, p+22.

Original entry on oeis.org

7, 29, 19, 41, 31, 53, 37, 59, 61, 83, 67, 89, 79, 101, 109, 131, 127, 149, 151, 173, 157, 179, 211, 233, 229, 251, 241, 263, 271, 293, 331, 353, 337, 359, 367, 389, 379, 401, 397, 419, 409, 431, 421, 443, 439, 461, 457, 479, 487, 509, 499, 521, 541, 563, 547

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

nonn

The two primes p and p+22 are not necessarily adjacent.

			The pairs are (7, 29), (19, 41), (31, 53) etc.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000040, A094343.

{#, # + 22} & /@ Select[Prime@ Range@ 100, PrimeQ@ # && PrimeQ[# + 22] &] // Flatten (* Michael De Vlieger, May 23 2016 *)

require 'prime'
ary = []
Prime.each(487447).each{|i| ary += [i, i + 22] if (i + 22).prime?}
p ary  # Seiichi Manyama, May 22 2016

Typo in definition edited by D. S. McNeil, Dec 10 2009

Entries verified and extended by D. S. McNeil, Dec 10 2009

A140445 List of prime pairs of form p, p + 10.

Original entry on oeis.org

3, 13, 7, 17, 13, 23, 19, 29, 31, 41, 37, 47, 43, 53, 61, 71, 73, 83, 79, 89, 97, 107, 103, 113, 127, 137, 139, 149, 157, 167, 163, 173, 181, 191, 223, 233, 229, 239, 241, 251, 271, 281, 283, 293, 307, 317, 337, 347, 349, 359, 373, 383, 379, 389, 409, 419, 421

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A023203 (1st bisection), A092146 (2nd bisection).

Cf. prime pairs of the form (p, p+k): A077800 (k=2), A094343 (k=4), A156274 (k=6), A156320 (k=8), this sequence (k=10), A156323 (k=12), A140446 (k=14), A272815 (k=16), A156328 (k=18), A272816 (k=20), A140447 (k=22).

i: 1: for k from 1 to 1200 do if isprim (k) and isprim (k+10) then a [ i ] : = k : a [ i + 1]: = k + 10 : i = i + 2 fi od : seq (a [ n ], n=1..i-1);

Flatten[{#,#+10}&/@Select[Prime[Range[100]],PrimeQ[#+10]&]]  (* Harvey P. Dale, Apr 11 2011 *)

Corrected by D. S. McNeil, Dec 10 2009

A272815 Prime pairs of the form (p, p+16).

Original entry on oeis.org

3, 19, 7, 23, 13, 29, 31, 47, 37, 53, 43, 59, 67, 83, 73, 89, 97, 113, 151, 167, 157, 173, 163, 179, 181, 197, 211, 227, 223, 239, 241, 257, 277, 293, 331, 347, 337, 353, 367, 383, 373, 389, 433, 449, 463, 479, 487, 503, 541, 557, 547, 563, 571

Offset: 1

Vincenzo Librandi, May 07 2016

p and p+16 are not necessarily consecutive primes: (1831, 1847) is the first pair of consecutive primes that belongs to the sequence.

			The prime pairs are (3, 19), (7, 23), (13, 29) etc.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000040, A049488.

Cf. prime pairs of the form (p, p+k): A077800 (k=2), A094343 (k=4), A156274 (k=6), A156320 (k=8), A140445 (k=10), A156323 (k=12), A140446 (k=14), this sequence (k=16), A156328 (k=18), A272816 (k=20), A140447 (k=22).

&cat [[p,p+16]: p in PrimesUpTo(1000) | IsPrime(p+16)];

Flatten[{#, # + 16}&/@Select[Prime[Range[200]], PrimeQ[# + 16] &]]

a(2n+1) = A049488(n+1).

A272816 Prime pairs of the form (p, p+20).

Original entry on oeis.org

3, 23, 11, 31, 17, 37, 23, 43, 41, 61, 47, 67, 53, 73, 59, 79, 83, 103, 89, 109, 107, 127, 131, 151, 137, 157, 173, 193, 179, 199, 191, 211, 251, 271, 257, 277, 263, 283, 293, 313, 311, 331, 317, 337, 347, 367, 353, 373, 359, 379, 389, 409, 401, 421

Offset: 1

Vincenzo Librandi, May 07 2016

p and p+20 are not necessarily consecutive primes: (887, 907) is the first pair of consecutive primes that belongs to the sequence.

			The prime pairs are (3, 23), (11, 31), (17, 37) etc.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000040, A153419.
Cf. similar sequences listed in A272815.
Prime pairs of the form (p, p+k): A077800 (k=2), A094343 (k=4), A156274 (k=6), A156320 (k=8), A140445 (k=10), A156323 (k=12), A140446 (k=14), A272815 (k=16), A156328 (k=18), this sequence (k=20), A140447 (k=22).

&cat [[p, p+20]: p in PrimesUpTo(1000) | IsPrime(p+20)];

Flatten[{#, # + 20}&/@Select[Prime[Range[200]], PrimeQ[# + 20] &]]

from gmpy2 import is_prime
for n in range(1000):
   if(is_prime(n) and is_prime(n+20)):
      print('{}, {}'.format(n,n+20),end=', ')
# Soumil Mandal, May 14 2016

a(2n+1) = A153419(n+1).

Edited by Bruno Berselli, May 12 2016

A111980 Union of pairs of consecutive primes p, q with q-p = 4.

Original entry on oeis.org

7, 11, 13, 17, 19, 23, 37, 41, 43, 47, 67, 71, 79, 83, 97, 101, 103, 107, 109, 113, 127, 131, 163, 167, 193, 197, 223, 227, 229, 233, 277, 281, 307, 311, 313, 317, 349, 353, 379, 383, 397, 401, 439, 443, 457, 461, 463, 467, 487, 491, 499, 503, 613, 617, 643

Offset: 1

Ray Chandler, Aug 24 2005

nonn

Essentially the same as A094343.
Union of A029710 and A031505.
Cf. A140546.

Flatten[Select[Partition[Prime[Range[200]],2,1],#[[2]]-#[[1]]==4&]]//Union (* Harvey P. Dale, Jul 09 2024 *)

A140448 List of prime pairs of form p, p+34.

Original entry on oeis.org

3, 37, 7, 41, 13, 47, 19, 53, 37, 71, 67, 101, 73, 107, 79, 113, 97, 131, 103, 137, 139, 173, 157, 191, 163, 197, 193, 227, 199, 233, 223, 257, 229, 263, 277, 311, 283, 317, 313, 347, 349, 383, 367, 401, 397, 431, 409, 443, 433, 467, 457, 491, 487, 521, 523

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2008

nonn

The two primes p and p+34 are not necessarily adjacent.

			The pairs are (3, 37), (7, 41), (13, 47), etc.

Cf. A000040, A094343.

Typos in definition and example corrected by D. S. McNeil, Dec 10 2009

Corrected by D. S. McNeil, Dec 10 2009

A339084 Smaller term p1 of the first of two consecutive cousin prime pairs (p1,p1+4) and (p2,p2+4) such that the distance (p2-p1) is a square.

Original entry on oeis.org

3, 127, 313, 1447, 2203, 2437, 2797, 3217, 4933, 5653, 6007, 7207, 7537, 7603, 7753, 8233, 10627, 11827, 12373, 20353, 22027, 22153, 23017, 23563, 25303, 27697, 27763, 29023, 29059, 29383, 31477, 32323, 32533, 32569, 32839, 33199, 33577, 35533, 36523, 37273, 41077

Offset: 1

Claude H. R. Dequatre, Nov 23 2020

Considering the 10^6 cousin prime pairs from (3,7) to (252115609,252115613), we note the following:
43617 sequence terms (4.4%) are linked to a distance between two consecutive cousin prime pairs which is a square.
List of the 9 classes of distances which are squares: 4,36,144,324,576,900,1296,1764,2304.
The distance 36 occurs with the highest frequency.
Distances linked to the first 50 terms of the sequence: 4,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,36,324,144,36,36,36,144,144,144,36,36,36,36,36,36,36,36,144,36,144,36,36,36
From the class 36, the frequency of the distances decreases when their size increases; the distance 4 linked to the first term of the sequence occurs only once.
See for comparison the sequence A338812.

			a(3)=313 is in the sequence because the two consecutive cousin prime pairs being (313,317) and (349,353), the distance between them is 349-313=36 which is a square (6^2).
613 is not in the sequence because the two consecutive cousin prime pairs being (613,617) and (643,647), the distance between them is (643-613)=30 which is not a square.

Cf. A023200, A046132, A094343.
Cf. A000290, A053320.
Cf. A176130, A161002, A161533, A161534, A138198, A338812.

lista(nn) = {my(last=3, p=7); forprime(q=11, nn, if(q-p==4, if (issquare(p-last), print1(last, ", ")); last = p;); p = q;);} \\ Michel Marcus, Nov 23 2020

Mat<-matrix(0,14000000,5)
primes<-generate_n_primes(14000000)
Mat[,1]<-c(primes)
a_n<-c()
Squares<-c()
Squares_sq<-c()
j=1
counter=0
while(j<=13999999){
  if(is_prime((Mat[j,1])+4) & is_prime((Mat[j+1,1]))+4){
    counter=counter+1
    Mat[counter,2]<-(Mat[j,1])
    Mat[counter,3]<-Mat[j,1]+4
    Mat[counter+1,2]<-(Mat[j+1,1])
    Mat[counter+1,3]<-Mat[j+1,1]+4
  }
  j=j+1
}
k=1
while(k<=1000000){
  dist<- Mat[k+1,2]-Mat[k,2]
  Mat[k,4]<-dist
  if(sqrt(dist)%%1==0){
    Mat[k,5]<-dist
    a_n<-append(a_n,Mat[k,2])
  }
  k=k+1
}
View(Mat)
View(a_n)

cp's OEIS Frontend

A140382 Duplicate of A094343.

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A140446 List of prime pairs of form p, p+14.

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A140447 List of prime pairs of form p, p+22.

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A140445 List of prime pairs of form p, p + 10.

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A272815 Prime pairs of the form (p, p+16).

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Magma

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A272816 Prime pairs of the form (p, p+20).

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A111980 Union of pairs of consecutive primes p, q with q-p = 4.

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Mathematica

A140448 List of prime pairs of form p, p+34.

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A339084 Smaller term p1 of the first of two consecutive cousin prime pairs (p1,p1+4) and (p2,p2+4) such that the distance (p2-p1) is a square.