cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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.

Examples

			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).

Links

Crossrefs

Cf. A242719, A242720, A242847, A246748.

Formula

Intersection of A245363 and A247280.

A247549 Numbers n for which A242720(n) = prime(n)*(prime(n)+8)+3.

Original entry on oeis.org

5, 32, 43, 79, 126, 142, 523, 576, 722, 771, 1026, 1152, 1234, 1402, 1442, 1480, 1623, 1630, 1767, 1814, 1829, 1962, 1995, 2062, 2084, 2353, 2705, 3104, 3174, 3355, 3588, 3718, 4005, 4035, 4126, 4266, 4581, 4616, 4785, 4854, 4859, 5068, 5131, 5145, 5164
Offset: 1

Views

Author

Vladimir Shevelev, Sep 19 2014

Keywords

Comments

prime(n)*(prime(n)+8) + 3, such that prime(n)+8 and prime(n)*(prime(n)+8)+2 are primes, is the third minimal possible value of A242720(n) after (prime(n)+1)^2 + 2, n>=3 (cf. A246824) and prime(n)*(prime(n)+4) + 3 (cf. A247280).

Crossrefs

Cf. A242719, A242720, A242847, A245363, A246748, A246824, A247011, A147280.

Formula

If n is in the sequence, then prime(n) == 1 (mod 10), A242720(n) == 12 (mod 100).

Extensions

More terms from Peter J. C. Moses, Sep 19 2014
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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