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A175839 Smallest runs of n*2-1 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 21:14 EDT 2022. Contains 354110 sequences. (Running on oeis4.)