A374179 a(n) is the least prime p such that the binary expansions of p and of the next prime q > p differ at exactly n positions, and p and q have the same binary length.

2, 11, 47, 139, 157, 191, 1151, 1531, 3067, 7159, 20479, 36857, 49139, 98299, 360439, 917503, 1310719, 786431, 6291449, 5242877, 20971507, 58720253, 83886053, 201326557, 335544301, 402653171, 3489660919, 1879048183, 5368709117, 25769803751, 21474836479, 77309411323

Offset

1,1

Links

Table of n, a(n) for n=1..32.

Example

  a(n): 2       11           47               139                157
   np   3       13           53               149                163
      [1 0]  [1 0 1 1]  [1 0 1 1 1 1]  [1 0 0 0 1 0 1 1]  [1 0 0 1 1 1 0 1]
      [1 1]  [1 1 0 1]  [1 1 0 1 0 1]  [1 0 0 1 0 1 0 1]  [1 0 1 0 0 0 1 1]
         ^      ^ ^        ^ ^   ^            ^ ^ ^ ^          ^ ^ ^ ^ ^
  n:     1       2            3                  4                 5

Prog

(Python)
from sympy import nextprime
def A374179(n):
    p, pb = 2, 2
    while (q:=nextprime(p)):
        if pb==(qb:=q.bit_length()) and (p^q).bit_count() == n:
            return p
        p, pb = q, qb  # Chai Wah Wu, Jul 10 2024

Crossrefs

Cf. A000120, A000788, A007088, A061712, A205510, A374178.

Sequence in context: A106980 A089682 A211671 * A198693 A178710 A050929

Adjacent sequences: A374176 A374177 A374178 * A374180 A374181 A374182

Keyword

nonn,base,new

Author

Hugo Pfoertner, Jul 09 2024

Status

approved