A374178 a(n) is the least prime p such that p and the next prime > p have exactly n common 1's in their binary expansion.

2, 5, 19, 29, 181, 359, 379, 983, 3821, 3581, 8179, 16111, 81901, 98297, 131059, 131063, 524269, 917471, 3145679, 4128763, 16744423, 16776187, 58720223, 117440381, 266330047, 468713467, 536870879, 1073741309, 2147483629, 4294967231, 8589410287, 33285865469

Offset

1,1

Comments

1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Example

  a(n): 2       5         19           29              181
   np   3       7         23           31              191
      [1 0]  [1 0 1]  [1 0 0 1 1]  [1 1 1 0 1]  [1 0 1 1 0 1 0 1]
      [1 1]  [1 1 1]  [1 0 1 1 1]  [1 1 1 1 1]  [1 0 1 1 1 1 1 1]
       ^      ^   ^    ^     ^ ^    ^ ^ ^   ^    ^   ^ ^   ^   ^
  n:   1        2          3            4               5

Prog

(Python)
from sympy import nextprime
def A374178(n):
    p = 2
    while (q:=nextprime(p)):
        if (p&q).bit_count() == n:
            return p
        p = q # Chai Wah Wu, Jul 08 2024

Crossrefs

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

Sequence in context: A184868 A077317 A092946 * A090700 A227632 A105889

Adjacent sequences: A374175 A374176 A374177 * A374179 A374180 A374181

Keyword

nonn,base,new

Author

Hugo Pfoertner, Jul 08 2024

Status

approved