A175839 Smallest runs of n*2-1 consecutive composites.

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

Offset: 1

Author

Grant Garcia, Sep 20 2010

Keywords

• easy
• nonn

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).

Examples

			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;
		

Links

• Wikipedia, Composite number

Crossrefs

Cf. A002808, A046933, A008950.

Programs

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)