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

Author

Hugo Pfoertner, Jul 08 2024

Keywords

• nonn
• base

Comments

1

Examples

			  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
		

Links

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

Crossrefs

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

Programs

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