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A317308 Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central peak. 1
2, 7, 17, 19, 29, 31, 47, 53, 67, 71, 73, 97, 101, 103, 127, 131, 157, 163, 167, 191, 193, 197, 199, 233, 239, 241, 251, 277, 281, 283, 293, 331, 337, 347, 349, 379, 383, 389, 397, 401, 439, 443, 449, 457, 461, 463, 499, 503, 509, 521, 523, 563, 569, 571, 577, 587, 593, 631, 641, 643, 647, 653, 659, 661 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also primes p such that both Dyck paths of the symmetric representation of sigma(p) have a central peak.

Note that the symmetric representation of sigma of an odd prime consists of two perpendicular bars connected by an irregular zig-zag path (see example).

Odd primes and the terms of this sequence are easily identifiable in the pyramid described in A245092 (see Links section).

For more information about the mentioned Dyck paths see A237593.

Equivalently, primes p such that the largest Dyck path of the symmetric representation of sigma(p) has an odd number of peaks.

LINKS

Table of n, a(n) for n=1..64.

Omar E. Pol, Perspective view of the pyramid (first 16 levels)

EXAMPLE

Illustration of initial terms:

--------------------------------------------------------

   p   sigma(p)   Diagram of the symmetry of sigma

--------------------------------------------------------

                    _         _                   _   _

                  _| |       | |                 | | | |

   2      3      |_ _|       | |                 | | | |

                             | |                 | | | |

                            _|_|                 | | | |

                          _|                     | | | |

                  _ _ _ _|                       | | | |

   7      8      |_ _ _ _|                       | | | |

                                                 | | | |

                                            _ _ _|_| | |

                                           |    _ _ _|_|

                                          _|   |

                                        _|  _ _|

                                    _ _|  _|

                                   |     |

                                   |  _ _|

                  _ _ _ _ _ _ _ _ _| |

  17     18      |_ _ _ _ _ _ _ _ _| |

                  _ _ _ _ _ _ _ _ _ _|

  19     20      |_ _ _ _ _ _ _ _ _ _|

.

For the first four terms of the sequence we can see in the above diagram that the largest Dyck path of the symmetric representation of sigma(p) has a central peak.

Compare with A317309.

CROSSREFS

Primes in A162917.

Also primes in A317303.

The union of this sequence and A317309 gives A000040.

Cf. A000203, A065091, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A239660, A239929, A239931, A239933, A244050, A245092, A262626.

Sequence in context: A006883 A023269 A023300 * A045378 A101568 A291528

Adjacent sequences:  A317305 A317306 A317307 * A317309 A317310 A317311

KEYWORD

nonn,changed

AUTHOR

Omar E. Pol, Aug 29 2018

STATUS

approved

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Last modified November 18 12:16 EST 2019. Contains 329261 sequences. (Running on oeis4.)