A383969 a(n) is the smallest even number m such that the set {m+1, m+3, m+5, ..., m+(2*n-1)} contains no prime numbers.

0, 24, 90, 114, 114, 114, 524, 524, 888, 1130, 1328, 1328, 1328, 1328, 1328, 1328, 9552, 15684, 15684, 15684, 15684, 19610, 19610, 19610, 19610, 31398, 31398, 31398, 31398, 31398, 31398, 31398, 31398, 31398, 31398, 155922, 155922, 155922, 155922, 155922, 155922, 155922

Offset: 1

Author

David James Sycamore, May 16 2025

Keywords

• nonn

Comments

For a(2) onward, consists of terms of A008950(n), perhaps repeated, based on the increase in records. So, higher terms may be easily computed using the b-files at A008950 and A002386. - Michael S. Branicky, May 23 2025

Examples

			a(1) = 0 since 0 is the smallest even number such that 0 + 1 = 1 is not prime
a(2) = 24 since there are no primes in {24+1, 24+3} = {25, 27} and no smaller even number has this property.
a(3) = 90 since there are no primes in {91, 93, 95}, and no smaller even number has this property.
		

Crossrefs

Cf. A000040, A002808, A018252, A008950, A002386.

Programs

Mathematica

k = 0; Table[While[AnyTrue[k + Range[2*n - 1], PrimeQ], k += 2]; k, {n, 42}] (* Michael De Vlieger, Jun 01 2025 *)

Python

from sympy import isprime
from itertools import count
def a(n): return next(m for m in count(0, 2) if all(not isprime(m+2*i+1) for i in range(n)))
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, May 23 2025

Extensions

a(4) and beyond from Michael S. Branicky, May 23 2025