A145472 -id:A145472 - cp's OEIS frontend

A145479 Primes p such that (31+p)/2 is prime.

3, 7, 31, 43, 103, 127, 163, 223, 271, 283, 331, 367, 523, 631, 643, 727, 787, 811, 883, 967, 1051, 1063, 1123, 1171, 1231, 1291, 1423, 1447, 1471, 1483, 1543, 1627, 1723, 1783, 1951, 1987, 2011, 2143, 2203, 2311, 2371, 2467, 2551, 2731, 2767, 2887, 3067

Offset: 1

Artur Jasinski, Oct 11 2008

nonn

All terms are congruent to 3 mod 4 and (with the exception of the first term) to 7 mod 12.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A092109, A145471, A145472, A145473, A145474, A145475, A145476, A145477, A145478, A145479, A155480.

aa = {}; k = 31; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(31+#)/2]&] (* Harvey P. Dale, Feb 05 2012 *)

list(n)=my(t=1, p, i=1); while(i2&&isprime((31+p)/2),print1(p, ", "))) \\ Anders Hellström, Jan 23 2017

A274507 Primes one more than the sum over a pair of prime numbers that differ by 8.

Original entry on oeis.org

19, 31, 67, 127, 151, 211, 271, 307, 547, 727, 787, 811, 907, 967, 991, 1447, 1531, 1831, 1867, 2131, 2467, 2647, 2887, 2971, 3967, 5107, 5227, 5407, 5431, 5827, 6091, 6427, 6451, 6607, 6907, 6991, 7411, 8191, 8431, 8707, 9511, 10111

Offset: 1

Debapriyay Mukhopadhyay, Jun 25 2016

nonn

Any prime p in this sequence is such that p = (p-9)/2 + (p+7)/2 + 1, where (p-9)/2 and (p+7)/2 are also primes and they differ by 8.

This sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Jul 08 2016

			19 = 5 + 13 + 1. Note that, (19-9)/2 = 5 and (19+7)/2 = 13 and the prime pairs 5 and 13 differ by 8.
31 = 11 + 19 + 1. Note that, (31-9)/2 = 11 and (31+7)/2 = 19 and the prime pairs 11 and 19 differ by 8.

Cf. A023202, A274506.

A subsequence of A068229 and also of A145472.

Select[2 # + 9 &@ Select[Prime@ Range[10^3], PrimeQ[# + 8] &], PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)

lista(nn)=forprime(p=3, nn, if (isprime(p+8) && isprime(q=2*p+9), print1(q, ", "))); \\ Michel Marcus, Jun 25 2016

cp's OEIS Frontend

A145479 Primes p such that (31+p)/2 is prime.

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