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

1,2

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.

Links

Table of n, a(n) for n=1..104.

Example

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.

Sequence in context: A040691 A040690 A040689 * A040693 A040692 A040694

Adjacent sequences: A140886 A140887 A140888 * A140890 A140891 A140892

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 06 2008

Extensions

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

Status

approved