A100813 Smallest number in base 2 which is also prime in base 2+n, or 0 if no such number exists.

10, 11, 10, 11, 10, 111, 1011, 11, 10, 11, 10, 101, 111, 11, 10, 11, 10, 101, 111, 11, 10, 101, 111011, 101, 111, 11, 10, 11, 10, 1011, 111, 10001, 1101, 11, 10, 111, 1011, 11, 10, 11, 10, 1011, 1101, 11, 10, 1011, 1100111, 111, 101001, 11, 10, 101, 111011, 101

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(6) = 111: 111 (base 2) = 7, which is prime; 111 (base 2+6) = 73, which is prime.

Mathematica

a = {}; Do[ k = 1; While[ ! PrimeQ[FromDigits[IntegerDigits[Prime[k], 2], 2 + n]], k++ ]; AppendTo[a, FromDigits[IntegerDigits[Prime[k], 2], 10]]; , {n, 50}]; a (* Ray Chandler, Jan 10 2005 *)

Prog

(Python)
from sympy import isprime, nextprime
def fd(s, b): return sum(b**i for i, si in enumerate(s[::-1]) if si=='1')
def a(n):
    p = 2
    while not isprime(fd(bin(p)[2:], n+2)): p = nextprime(p)
    return int(bin(p)[2:])
print([a(n) for n in range(1, 55)]) # Michael S. Branicky, Aug 20 2022

Crossrefs

Sequence in context: A020509 A373696 A103181 * A085209 A085217 A085210

Adjacent sequences: A100810 A100811 A100812 * A100814 A100815 A100816

Keyword

base,nonn

Author

Ray G. Opao, Jan 05 2005

Extensions

Corrected and extended by Ray Chandler, Jan 10 2005

a(51) and beyond from Michael S. Branicky, Aug 09 2022

Status

approved