A396573 Primes p such that the gap to the next prime is strictly less than floor(log_2(p)).

11, 17, 29, 37, 41, 43, 59, 67, 71, 79, 97, 101, 103, 107, 109, 127, 131, 137, 149, 151, 157, 163, 167, 173, 179, 191, 193, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 277, 281, 307, 311, 313, 331, 347, 349, 353, 367, 373, 379, 383, 397, 419, 431, 433, 439, 443, 457, 461, 463

Offset

1,1

Comments

Terms are {p in primes | g < floor(log_2(p)) }, where g is the forward prime gap.

Links

Table of n, a(n) for n=1..60.

Example

For p = 11: next prime is 13; gap = 2, floor(log_2(11)) = 3, 2 < 3 is true, so 11 is included.
For p = 13: next prime is 17; gap = 4, floor(log_2(13)) = 3, 4 < 3 is false, so 13 is excluded.

Mathematica

Select[Prime[Range[PrimePi[463]]], NextPrime[#]-#<Floor[Log2[#]]&] (* James C. McMahon, Jun 06 2026 *)

Prog

(Python)
from sympy import nextprime
def A000523(n): return n.bit_length() - 1
def sub_dimensional_primes(limit):
    sub_primes = []
    p = 11
    while p < limit:
        if nextprime(p) - p < A000523(p):
            sub_primes.append(p)
        p = nextprime(p)
    return sub_primes
print(sub_dimensional_primes(500))

Crossrefs

Cf. A000040 (primes), A000523 (floor(log_2)), A151800 (next prime), A396203, A396279, A396282.

Sequence in context: A110055 A240095 A105886 * A225493 A051634 A038918

Adjacent sequences: A396570 A396571 A396572 * A396574 A396577 A396579

Keyword

nonn

Author

Sajid Hussain, May 29 2026

Status

approved