A063910 -id:A063910 - cp's OEIS frontend

A145472 Primes p such that (p+7)/2 is prime.

3, 7, 19, 31, 67, 79, 127, 139, 151, 199, 211, 271, 307, 379, 439, 547, 607, 619, 691, 727, 739, 751, 787, 811, 859, 907, 919, 967, 991, 1039, 1087, 1231, 1279, 1447, 1459, 1471, 1531, 1567, 1699, 1747, 1759, 1831, 1867, 1987, 2011, 2131, 2179, 2239, 2251

Offset: 1

Artur Jasinski, Oct 11 2008

All these primes are congruent to 3 mod 4 and (with the exception of the first one) to 7 mod 12.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A092109, A145471-A145480, A063910.

[p: p in PrimesUpTo(2500)| IsPrime((p + 7) div 2)]; // Vincenzo Librandi, Feb 04 2013

aa = {}; k = 7; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+7)/2]&] (* Harvey P. Dale, Jan 11 2020 *)

list(n)=my(t=1, p, i=1); while(i2&&isprime((7+p)/2), print1(n, ", "))) \\Anders Hellström, Jan 23 2017

list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+7)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

A290838 a(n) = smallest prime p such that 2p - 2n + 1 is prime.

Original entry on oeis.org

2, 2, 3, 5, 5, 7, 7, 13, 11, 11, 11, 13, 13, 19, 17, 17, 17, 19, 19, 37, 23, 23, 23, 29, 29, 31, 29, 29, 29, 31, 31, 37, 37, 41, 37, 37, 37, 43, 41, 41, 41, 43, 43, 61, 47, 47, 47, 53, 53, 67, 53, 53, 53, 59, 59, 61, 59, 59, 59, 61, 61, 67, 67, 71, 67, 67, 67, 73

Offset: 0

XU Pingya, Aug 11 2017

a(n) > n. - Iain Fox, Nov 13 2017

Iain Fox, Table of n, a(n) for n = 0..20000

Cf. A005382, A063908, A063909, A063910, A063911, A063912, A063913, A020483, A290839.

Table[j=0; found=False; While[!found,j++; found=PrimeQ[2Prime[j]-2n+1] && 2Prime[j]-2n+1>0]; Prime[j],{n,67}]
(* Second program: *)
Table[SelectFirst[Prime@ Range[n^2], And[# > 0, PrimeQ@ #] &[2 # - 2 n + 1] &], {n, 67}] (* Michael De Vlieger, Aug 14 2017 *)

a(n) = {my(p=2); while(!isprime(2*p-2*n+1), p = nextprime(p+1)); p; } \\ Michel Marcus, Aug 12 2017

a(n) = forprime(p=n+1, , if(isprime(2*p - 2*n + 1), return(p))) \\ Iain Fox, Nov 13 2017

a(-n) = A290839(n+1) - Iain Fox, Dec 14 2017

a(0) prepended by Iain Fox, Dec 14 2017

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A145472 Primes p such that (p+7)/2 is prime.

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A290838 a(n) = smallest prime p such that 2p - 2n + 1 is prime.

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