A247279 Numbers n such that A242720(n) = prime(n)*(prime(n)+4)+3 and A242719(n) - A242720(n) = 2*(prime(n)-1).

19, 920, 2869, 4704, 8125, 10194, 10939, 17588, 22661, 29856, 31178, 31779, 53624, 59035, 61931, 66944, 72104, 81247, 91456, 98840, 103631, 106187, 117959, 123535, 131824, 133446, 168209, 184888, 189389, 214743, 215352, 218421, 218799, 227088, 237917, 245854

Offset

1,1

Comments

The sequence is infinite if there are infinitely many primes p_n such that p_n+4, p_n+6, p_n*(p_n+4)+2, p_n*(p_n+6)-2 are primes, but p_n^2-2 is not prime.

If the sequence A246748 is also infinite, then these two sequences show that the difference A242720(n) - A242719(n) changes its sign infinitely many times.

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Formula

Intersection of A245363 and A247280.

Example

If n=920, prime(920)=7207, we have A242720(920) = 7207*7211+3 = 51969680 and A242919(920) -  A242920(920) = 51984092 - 51969680 = 14412 = 2*(prime(920)-1).

Crossrefs

Cf. A242719, A242720, A242847, A246748.

Sequence in context: A368789 A005535 A171226 * A192569 A238740 A285862

Adjacent sequences: A247276 A247277 A247278 * A247280 A247281 A247282

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Sep 11 2014

Status

approved