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 A256262 Number of successive odd numbers that are not twin primes and number of successive twin primes, interleaved. 3
 1, 3, 1, 2, 1, 2, 4, 2, 4, 2, 7, 2, 4, 2, 13, 2, 1, 2, 13, 2, 4, 2, 13, 2, 4, 2, 1, 2, 13, 2, 4, 2, 13, 2, 4, 2, 13, 2, 16, 2, 34, 2, 4, 2, 13, 2, 28, 2, 22, 2, 13, 2, 7, 2, 10, 2, 7, 2, 73, 2, 4, 2, 1, 2, 13, 2, 10, 2, 67, 2, 4, 2, 7, 2, 4, 2, 13, 2, 28, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See also both A256252 and A256253 which contain similar diagrams. LINKS EXAMPLE Consider an irregular array in which the odd-indexed rows list successive odd numbers that are not twin primes (A255763) and the even-indexed rows list successive twin primes (A001097), in the sequence of odd numbers (A005408), as shown below: 1; 3, 5, 7; 9; 11, 13; 15; 17; 19; 21, 23, 25, 27; 39, 31; ... a(n) is the length of the n-th row. . Illustration of the first 16 regions of the diagram of the symmetric representation of odd numbers that are not twin primes (A255763) and of twin primes (A001097). .            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .           |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _  |   31 .           |_ _ _ _ _ _ _ _ _ _ _ _ _ _  | |   29 .           | | | | |_ _ _ _ _ _ _ _ _  | | |   19 .           | | | | |_ _ _ _ _ _ _ _  | | | |   17 .           | | | | | |_ _ _ _ _ _  | | | | |   13 .           | | | | | |_ _ _ _ _  | | | | | |   11 .           | | | | | | |_ _ _  | | | | | | |    7 .           | | | | | | |_ _  | | | | | | | |    5 .   A255763 | | | | | | |_  | | | | | | | | |    3 .      1    | | | | | | |_|_|_|_| | | | | | | A001097 .      9    | | | | | |_ _ _ _ _|_|_| | | | | .     15    | | | | |_ _ _ _ _ _ _ _|_|_| | | .     21    | | | |_ _ _ _ _ _ _ _ _ _ _| | | .     23    | | |_ _ _ _ _ _ _ _ _ _ _ _| | | .     25    | |_ _ _ _ _ _ _ _ _ _ _ _ _| | | .     27    |_ _ _ _ _ _ _ _ _ _ _ _ _ _|_|_| . 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..8: . .                         |_ _ _ .                               |_ _ .                                   |_ _ .                                       | .                                       | .                                       | .                                       |_ _ . The sequence begins:      1,3,1,2,1,2,4,2,... . PROG (PARI) istwin(n) = isprime(n) && (isprime(n-2) || isprime(n+2)); lista(nn) = {my(nb = 1, istp = 0); forstep (n=3, nn, 2, if (bitxor(istp, ! istwin(n)), nb++, print1(nb, ", "); nb = 1; istp = ! istp); ); } \\ Michel Marcus, May 25 2015 CROSSREFS Cf. A005408, A001097, A256252, A256253, A255763. Sequence in context: A082882 A188902 A324081 * A332929 A157520 A325116 Adjacent sequences:  A256259 A256260 A256261 * A256263 A256264 A256265 KEYWORD nonn AUTHOR Omar E. Pol, Mar 31 2015 EXTENSIONS More terms from Michel Marcus, May 25 2015 STATUS approved

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Last modified June 4 11:28 EDT 2020. Contains 334825 sequences. (Running on oeis4.)