A164510 First differences of A071904 (Odd composite numbers).

6, 6, 4, 2, 6, 2, 4, 6, 4, 2, 4, 2, 6, 2, 4, 6, 2, 4, 4, 2, 4, 2, 2, 4, 6, 6, 4, 2, 2, 2, 2, 2, 4, 4, 2, 6, 2, 2, 2, 6, 2, 4, 2, 4, 4, 2, 4, 2, 6, 2, 2, 2, 6, 6, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 6, 4, 2, 6, 2, 2, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 6, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 6, 4, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 6

Offset

1,1

Comments

Are all terms <=6?

This is A067970 without its first term. [R. J. Mathar, Aug 17 2009]

Yes, all terms are at most 6. For a value of 8, we have to have p, p+2, p+4 all prime, and this is possible only for p=3. As a result, 1 would have to be an odd composite number, which it is not. Therefore all terms are <=6. [J. Lowell, Aug 17 2009]

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Joel E. Cohen and Dexter Senft, Gaps of size 2, 4, and (conditionally) 6 between successive odd composite numbers occur infinitely often, Notes Num. Theor. Disc. Math. (2025) Vol. 31, No. 3, 494-503. See p. 495.

Mathematica

Differences@ Select[Range[1, 360, 2], CompositeQ] (* Michael De Vlieger, Aug 29 2025 *)

Prog

(Python)
from sympy import primepi, isprime
def A164510(n):
    m, k = n, primepi(n+1) + n + (n+1>>1)
    while m != k:
        m, k = k, primepi(k) + n + (k>>1)
    for d in range(2, 7, 2):
        if not isprime(m+d):
            return d # Chai Wah Wu, Aug 02 2024

Crossrefs

Cf. A071904.

Sequence in context: A094888 A159702 A255188 * A019957 A099405 A090966

Adjacent sequences: A164507 A164508 A164509 * A164511 A164512 A164513

Keyword

nonn

Author

Zak Seidov, Aug 14 2009

Status

approved