A140446 -id:A140446 - cp's OEIS frontend

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

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

A329262 Prime pairs of the form (30k - 7, 30k + 7).

Original entry on oeis.org

23, 37, 53, 67, 83, 97, 113, 127, 263, 277, 293, 307, 353, 367, 383, 397, 443, 457, 563, 577, 593, 607, 743, 757, 773, 787, 863, 877, 953, 967, 983, 997, 1103, 1117, 1223, 1237, 1283, 1297, 1433, 1447, 1553, 1567, 1583, 1597, 1613, 1627

Offset: 1

Harry E. Neel, Nov 09 2019

The terms of this sequence are created by pairing the terms of the primes when the terms 30k - 7 and 30k + 7 are both prime. As has been pointed out, it is only a guess as to whether, or not, that (like the twin primes, etc.) there is or is not an infinite number of these pairings.

			As 4 * 30 - 7 = 113 and 4 * 30 + 7 = 127 are prime, both 113 and 127 are in the sequence. - _David A. Corneth_, Nov 10 2019

Cf. A140446, A153417, A007510.

Odd- (resp. even-) indexed terms are a subsequence of A132235 (resp. A132231).

&cat[[30*k-7] cat [30*k+7]:k in [1..60]|IsPrime(30*k-7) and IsPrime(30*k+7)]; // Marius A. Burtea, Nov 17 2019

Select[Prime[Range[1000]], MemberQ[{7, 23}, Mod[#, 30]] &] (* Jinyuan Wang, Nov 16 2019 *)
Flatten[Select[Table[30n + {-7, 7}, {n, 90}], PrimeQ[#[[1]]] && PrimeQ[#[[2]]] &]] (* Alonso del Arte, Dec 07 2019 *)

first(n) = n+=(n%2); my(res=List(),todo=n); for(i=1,oo, if(isprime(30*i-7) && isprime(30*i+7), listput(res,30*i-7); listput(res,30*i+7); todo-=2; if(todo<=0, return(res)))) \\ David A. Corneth, Nov 10 2019

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Python

Formula

Extensions

A329262 Prime pairs of the form (30k - 7, 30k + 7).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

Mathematica

PARI