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%I #27 Dec 31 2020 11:11:15
%S 0,0,1,1,2,1,2,2,2,2,3,2,3,3,3,3,4,3,4,4,4,4,5,4,5,5,5,5,6,5,6,6,6,6,
%T 7,6,7,7,7,7,8,7,8,8,8,8,9,8,9,9,9,9,10,9,10,10,10,10,11,10,11,11,11,
%U 11,12,11,12,12,12,12,13,12,13,13,13,13,14,13,14,14,14,14,15,14,15,15,15,15,16,15,16,16,16,16,17,16
%N a(1)=0; a(2)=0; for n>2: a(n) = A237591(n,2) = A237593(n,2).
%C n is an odd prime if and only if a(n) = 1 + a(n-1) and A237591(n,k) = A237591(n-1,k) for the values of k distinct of 2.
%C For k > 1 there are five numbers k in the sequence.
%C For more information see A237593.
%e Apart from the initial two zeros the sequence can be written as an array T(j,k) with 6 columns, where row j is [j, j, j+1, j, j+1, j+1], as shown below:
%e 1, 1, 2, 1, 2, 2;
%e 2, 2, 3, 2, 3, 3;
%e 3, 3, 4, 3, 4, 4;
%e 4, 4, 5, 4, 5, 5;
%e 5, 5, 6, 5, 6, 6;
%e 6, 6, 7, 6, 7, 7;
%e 7, 7, 8, 7, 8, 8;
%e 8, 8, 9, 8, 9, 9;
%e 9, 9, 10, 9, 10, 10;
%e 10, 10, 11, 10, 11, 11;
%e 11, 11, 12, 11, 12, 12;
%e 12, 12, 13, 12, 13, 13;
%e 13, 13, 14, 13, 14, 14;
%e 14, 14, 15, 14, 15, 15;
%e 15, 15, 16, 15, 16, 16;
%e ...
%e Illustration of initial terms:
%e Row _
%e 1 _| |0
%e 2 _| _|0
%e 3 _| |1|
%e 4 _| _|1|
%e 5 _| |2 _|
%e 6 _| _|1| |
%e 7 _| |2 | |
%e 8 _| _|2 _| |
%e 9 _| |2 | _|
%e 10 _| _|2 | | |
%e 11 _| |3 _| | |
%e 12 _| _|2 | | |
%e 13 _| |3 | _| |
%e 14 _| _|3 _| | _|
%e 15 _| |3 | | | |
%e 16 _| _|3 | | | |
%e 17 _| |4 _| _| | |
%e 18 _| _|3 | | | |
%e 19 _| |4 | | _| |
%e 20 _| _|4 _| | | _|
%e 21 _| |4 | _| | | |
%e 22 _| _|4 | | | | |
%e 23 _| |5 _| | | | |
%e 24 _| _|4 | | _| | |
%e 25 _| |5 | _| | | |
%e 26 | |5 | | | | |
%e ...
%e The figure represents the triangle A237591 in which the numbers of horizontal cells in the second geometric region gives this sequence, for n > 2.
%e Note that this is also the second geometric region in the front view of the stepped pyramid described in A245092. For more information see also A237593.
%Y Cf. A000040, A236104, A235791, A237048, A237591, A237593, A261350, A261699.
%K nonn,tabf,easy
%O 1,5
%A _Omar E. Pol_, Aug 24 2015