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

1,1

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