cp's OEIS Frontend

A256252 Number of successive odd noncomposite numbers A006005 and number of successive odd composite numbers A071904, interleaved.

%I A256252 #30 Jun 11 2015 10:26:36
%S A256252 4,1,2,1,2,1,1,2,2,2,1,1,2,1,1,2,1,2,2,2,1,1,2,2,1,1,1,2,1,3,1,1,2,1,
%T A256252 2,1,1,6,1,1,1,2,2,4,2,2,1,2,1,1,1,2,1,2,2,4,2,1,2,5,1,5,1,1,2,1,1,2,
%U A256252 2,4,1,2,1,2,1,2,2,2,1,1,2,4,1,6,1,1,2,1,1,6,1,2,1,4,2,1,1,2,1,3,1,2,1,2
%N A256252 Number of successive odd noncomposite numbers A006005 and number of successive odd composite numbers A071904, interleaved.
%C A256252 See also A256253 and A256262 which contain similar diagrams.
%F A256252 a(n) = A256253(n+1), n >= 2.
%e A256252 Consider an irregular array in which the odd-indexed rows list successive odd noncomposite numbers (A006005) and the even-indexed rows list successive odd composite numbers (A071904), in the sequence of odd numbers (A005408), as shown below:
%e A256252 1, 3, 5, 7;
%e A256252 9;
%e A256252 11, 13;
%e A256252 15;
%e A256252 17; 19;
%e A256252 21,
%e A256252 23;
%e A256252 25, 27;
%e A256252 39, 31;
%e A256252 ...
%e A256252 a(n) is the length of the n-th row.
%e A256252 .
%e A256252 Illustration of the first 16 regions of the diagram of the symmetric representation of odd noncomposite numbers A006005 and odd composite numbers A071904:
%e A256252 .            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A256252 .           |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _  |   31
%e A256252 .           |_ _ _ _ _ _ _ _ _ _ _ _ _ _  | |   29
%e A256252 .           | | |_ _ _ _ _ _ _ _ _ _ _  | | |   23
%e A256252 .           | | | |_ _ _ _ _ _ _ _ _  | | | |   19
%e A256252 .           | | | |_ _ _ _ _ _ _ _  | | | | |   17
%e A256252 .           | | | | |_ _ _ _ _ _  | | | | | |   13
%e A256252 .           | | | | |_ _ _ _ _  | | | | | | |   11
%e A256252 .           | | | | | |_ _ _  | | | | | | | |    7
%e A256252 .           | | | | | |_ _  | | | | | | | | |    5
%e A256252 .           | | | | | |_  | | | | | | | | | |    3
%e A256252 .   A071904 | | | | | |_|_|_|_| | | | | | | |    1
%e A256252 .      9    | | | | |_ _ _ _ _|_|_| | | | | | A006005
%e A256252 .     15    | | | |_ _ _ _ _ _ _ _|_|_| | | |
%e A256252 .     21    | | |_ _ _ _ _ _ _ _ _ _ _|_| | |
%e A256252 .     25    | |_ _ _ _ _ _ _ _ _ _ _ _ _| | |
%e A256252 .     27    |_ _ _ _ _ _ _ _ _ _ _ _ _ _|_|_|
%e A256252 .
%e A256252 a(n) is also the length of the n-th boundary segment in the zig-zag path of the above diagram, between the two types of numbers, as shown below for n = 1..9:
%e A256252 .                      _ _ _ _
%e A256252 .                             |_ _
%e A256252 .                                 |_ _
%e A256252 .                                     |_
%e A256252 .                                       |
%e A256252 .                                       |_ _
%e A256252 .
%e A256252 The sequence begins:      4,1,2,1,2,1,1,2,2,...
%e A256252 .
%o A256252 (PARI) lista(nn) = {my(nb = 1, isc = 0); forstep (n=3, nn, 2, if (bitxor(isc, isprime(n)), nb++, print1(nb, ", "); nb = 1; isc = ! isc););} \\ _Michel Marcus_, May 25 2015
%Y A256252 Cf. A005408, A006005, A071904, A256253, A256262.
%K A256252 nonn
%O A256252 1,1
%A A256252 _Omar E. Pol_, Mar 30 2015