A140889 Lengths of runs of consecutive primes and composites in A008364.

1, 26, 1, 4, 1, 5, 1, 3, 1, 4, 1, 1, 1, 6, 1, 1, 1, 7, 1, 1, 1, 4, 2, 2, 1, 4, 1, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 4, 1, 1, 1, 2, 1, 3, 1, 2, 3, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 3, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 2, 2, 1, 1, 1, 2, 2, 1, 5, 2, 4, 2, 4, 3, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 06 2008

Keywords

• nonn

Comments

Primes can be classified according to their remainder modulo 210: remainder 1 (A073102), 11..113 (primes), 121 (composite), 127..139 (primes), 143 (composite), 149..167 (primes), 169 (composite), 173..181 (primes), 187 (composite), 191..199 (primes), or 209 (composite). In the sequence A008364 of all numbers (prime or composite) in any of these remainder classes, we look for runs of numbers that are successively prime or composite and place the lengths of these runs in this sequence.

Examples

			Groups of runs in A008364 are (1), (11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113), (121), (127, 131, 137, 139), (143), (149, 151, ... ), which is 1 composite followed by 26 primes followed by 1 composite followed by 4 primes etc.
		

Crossrefs

Cf. A140378.

Extensions

First number in the comment corrected and entries checked by R. J. Mathar, Apr 28 2010