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A140378
Lengths of runs of consecutive primes and nonprimes in A007775.
3
1, 12, 1, 6, 1, 3, 1, 6, 2, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 4, 2, 1, 2, 6, 1, 1, 1, 1, 1, 6, 2, 1, 2, 4, 3, 2, 2, 4, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 2, 1, 3, 1, 4, 2, 1, 1, 2, 2, 3, 2, 2, 4, 2, 2, 1, 1, 4, 2, 1, 1, 4, 1, 3, 2, 1, 1, 3, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 2, 2, 2
OFFSET
1,2
COMMENTS
Primes can be classified according to their remainder modulo 30: remainder 1 (A136066), 7 (A132231), 11 (A132232), 13 (A132233), 17 (A039949), 19 (A132234), 23 (A132235), or 29 (A132236). In the sequence A007775 of all numbers (prime or nonprime) in any of these remainder classes, we look for runs of numbers that are successively prime or nonprime and place the lengths of these runs in this sequence.
EXAMPLE
Groups of runs in A007775 are (1), (7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47), (49), (53, 59, 61, 67, 71, 73), (77), (79, 83,...), which is 1 nonprime followed by 12 primes followed by 1 nonprime followed by 6 primes etc.
MAPLE
A007775 := proc(n) option remember ; local a; if n = 1 then 1; else for a from A007775(n-1)+1 do if a mod 2 <>0 and a mod 3 <>0 and a mod 5 <> 0 then RETURN(a) ; fi ; od: fi ; end: A := proc() local al, isp, n; al := 0: isp := false ; n := 1: while n< 300 do a := A007775(n) ; if isprime(a) <> isp then printf("%d, ", al) ; al := 1; isp := not isp ; else al := al+1 ; fi ; n := n+1: od: end: A() ; # R. J. Mathar, Jun 16 2008
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Jun 16 2008
STATUS
approved