cp's OEIS Frontend

A317308 Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central peak.

%I A317308 #37 Nov 11 2019 00:52:27
%S A317308 2,7,17,19,29,31,47,53,67,71,73,97,101,103,127,131,157,163,167,191,
%T A317308 193,197,199,233,239,241,251,277,281,283,293,331,337,347,349,379,383,
%U A317308 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
%N A317308 Primes p such that the largest Dyck path of the symmetric representation of sigma(p) has a central peak.
%C A317308 Also primes p such that both Dyck paths of the symmetric representation of sigma(p) have a central peak.
%C A317308 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).
%C A317308 Odd primes and the terms of this sequence are easily identifiable in the pyramid described in A245092 (see Links section).
%C A317308 For more information about the mentioned Dyck paths see A237593.
%C A317308 Equivalently, primes p such that the largest Dyck path of the symmetric representation of sigma(p) has an odd number of peaks.
%H A317308 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr05.jpg">Perspective view of the pyramid (first 16 levels)</a>
%e A317308 Illustration of initial terms:
%e A317308 --------------------------------------------------------
%e A317308    p   sigma(p)   Diagram of the symmetry of sigma
%e A317308 --------------------------------------------------------
%e A317308                     _         _                   _   _
%e A317308                   _| |       | |                 | | | |
%e A317308    2      3      |_ _|       | |                 | | | |
%e A317308                              | |                 | | | |
%e A317308                             _|_|                 | | | |
%e A317308                           _|                     | | | |
%e A317308                   _ _ _ _|                       | | | |
%e A317308    7      8      |_ _ _ _|                       | | | |
%e A317308                                                  | | | |
%e A317308                                             _ _ _|_| | |
%e A317308                                            |    _ _ _|_|
%e A317308                                           _|   |
%e A317308                                         _|  _ _|
%e A317308                                     _ _|  _|
%e A317308                                    |     |
%e A317308                                    |  _ _|
%e A317308                   _ _ _ _ _ _ _ _ _| |
%e A317308   17     18      |_ _ _ _ _ _ _ _ _| |
%e A317308                   _ _ _ _ _ _ _ _ _ _|
%e A317308   19     20      |_ _ _ _ _ _ _ _ _ _|
%e A317308 .
%e A317308 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.
%e A317308 Compare with A317309.
%Y A317308 Primes in A162917.
%Y A317308 Also primes in A317303.
%Y A317308 The union of this sequence and A317309 gives A000040.
%Y A317308 Cf. A000203, A065091, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A239660, A239929, A239931, A239933, A244050, A245092, A262626.
%K A317308 nonn
%O A317308 1,1
%A A317308 _Omar E. Pol_, Aug 29 2018