A231935 Greatest prime Q < 2*n such that 2*n-Q=P prime < Q starting at n=4.

5, 7, 7, 11, 13, 13, 17, 19, 19, 23, 23, 23, 29, 31, 31, 31, 37, 37, 41, 43, 43, 47, 47, 47, 53, 53, 53, 59, 61, 61, 61, 67, 67, 71, 73, 73, 73, 79, 79, 83, 83, 83, 89, 89, 89, 79, 97, 97, 101, 103, 103, 107, 109, 109, 113, 113, 113, 109, 113, 113, 109, 127, 127

Offset

4,1

Comments

All the primes >3 appear at least once in the sequence.

When a prime appears only once in the sequence, it is the smaller prime of a twin pair, but the smaller prime of a twin pair may be present more than once.

When a prime Q is present only once in the sequence as the smaller prime of a twin pair Q,Q+2 P=3=2*n-Q.

The primes Q are mainly in increasing order with repetitions, if the gap between two consecutive primes is > 6 there is at least one prime placed in decreasing order.

There are always 2 consecutive primes Q1 and Q2 with Q2 the greatest < 2*n for n>3, and as n increases the gap Q2-Q1 may increase also, but the total number of odd prime numbers P increases as 2*n/(2+log(n))and the gaps as 2+log(n) so it seems there are enough P candidates < Q/2 such that P+Q=2*n.

Links

Pierre CAMI, Table of n, a(n) for n = 4..10003

Mathematica

gpq[n_]:=Module[{q=NextPrime[2n, -1]}, While[!PrimeQ[2n-q], q=NextPrime[ q, -1]]; q]; Array[gpq, 70, 4] (* Harvey P. Dale, May 09 2018 *)

Crossrefs

Sequence in context: A114521 A258653 A159482 * A216835 A033932 A144186

Adjacent sequences: A231932 A231933 A231934 * A231936 A231937 A231938

Keyword

nonn

Author

Pierre CAMI, Nov 15 2013

Status

approved