

A175839


Smallest runs of n*21 consecutive composites.


0



4, 8, 9, 10, 24, 25, 26, 27, 28, 90, 91, 92, 93, 94, 95, 96, 114, 115, 116, 117, 118, 119, 120, 121, 122, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126
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OFFSET

1,1


COMMENTS

Even lengths of runs of composites are omitted, as nontrivial runs always have odd lengths (see A046933).
Run 5 (starting at 114) has 13 consecutive composites and is repeated in runs 6 and 7. Run 8 starts at 524 = A008950(6).


LINKS

Table of n, a(n) for n=1..49.
Wikipedia, Composite number


EXAMPLE

Run 1 has length 1; the first composite is 4.
Run 2 has length 3; the first three consecutive composites are 8, 9, and 10.
Run 3 has length 5; the first five consecutive composites are 24, 25, 26, 27, and 28.
4;
8, 9, 10;
24, 25, 26, 27, 28;
90, 91, 92, 93, 94, 95, 96;
114, 115, 116, 117, 118, 119, 120, 121, 122;
114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124;
114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126;


PROG

(Python)
from sympy import isprime
out = []
run = 1
for n in range(4, 10000):
isrun = True
for o in range(run): isrun *= not isprime(n + o  run)
if isrun:
for o in range(run): out.append(n + o  run)
run += 2
print(out)


CROSSREFS

Cf. A002808, A046933, A008950.
Sequence in context: A073042 A094349 A118715 * A226085 A104623 A228653
Adjacent sequences: A175836 A175837 A175838 * A175840 A175841 A175842


KEYWORD

easy,nonn


AUTHOR

Grant Garcia, Sep 20 2010


STATUS

approved



