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 A256253 Number of successive odd nonprimes A014076 and number of successive odd primes A065091, interleaved. 3
 1, 3, 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See also A256252 and A256262 which contain similar diagrams. LINKS FORMULA a(n) = A256252(n-1), n >= 3. EXAMPLE Consider an irregular array in which the odd-indexed rows list successive odd nonprimes (A014076) and the even-indexed rows list successive odd primes (A065091), 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 nonprimes (A014076) and of odd primes (A065091): .            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .           |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _  |   31 .           |_ _ _ _ _ _ _ _ _ _ _ _ _ _  | |   29 .           | | |_ _ _ _ _ _ _ _ _ _ _  | | |   23 .           | | | |_ _ _ _ _ _ _ _ _  | | | |   19 .           | | | |_ _ _ _ _ _ _ _  | | | | |   17 .           | | | | |_ _ _ _ _ _  | | | | | |   13 .           | | | | |_ _ _ _ _  | | | | | | |   11 .           | | | | | |_ _ _  | | | | | | | |    7 .           | | | | | |_ _  | | | | | | | | |    5 .   A014076 | | | | | |_  | | | | | | | | | |    3 .      1    | | | | | |_|_|_|_| | | | | | | | A065091 .      9    | | | | |_ _ _ _ _|_|_| | | | | | .     15    | | | |_ _ _ _ _ _ _ _|_|_| | | | .     21    | | |_ _ _ _ _ _ _ _ _ _ _|_| | | .     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..10: . .                       |_ _ _ .                             |_ _ .                                 |_ _ .                                     |_ .                                       | .                                       |_ _ . The sequence begins:    1,3,1,2,1,2,1,1,2,2,... . PROG (PARI) lista(nn) = {my(nb = 1, isp = 0); forstep (n=3, nn, 2, if (bitxor(isp, ! isprime(n)), nb++, print1(nb, ", "); nb = 1; isp = ! isp); ); } \\ Michel Marcus, May 25 2015 CROSSREFS Cf. A005408, A014076, A047846, A065091, A175632, A251092, A256252, A256134, A256262. Sequence in context: A212305 A205555 A165913 * A288818 A319658 A276988 Adjacent sequences:  A256250 A256251 A256252 * A256254 A256255 A256256 KEYWORD nonn AUTHOR Omar E. Pol, Mar 30 2015 STATUS approved

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Last modified October 19 21:08 EDT 2019. Contains 328228 sequences. (Running on oeis4.)