A098957 Decimal value of the reverse binary expansion of the prime numbers.

1, 3, 5, 7, 13, 11, 17, 25, 29, 23, 31, 41, 37, 53, 61, 43, 55, 47, 97, 113, 73, 121, 101, 77, 67, 83, 115, 107, 91, 71, 127, 193, 145, 209, 169, 233, 185, 197, 229, 181, 205, 173, 253, 131, 163, 227, 203, 251, 199, 167, 151, 247, 143, 223, 257, 449, 353, 481, 337

Offset

1,2

Comments

15 of the first 16 terms happen to be prime. As terms increase, the preponderance of primes apparently decreases.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..6542

Formula

a(n) = decimal(reverse(binary(prime(n)))) where prime(n) is the n-th prime.

a(n) = A030101(A000040(n)). - Rémy Sigrist, Oct 19 2022

Example

a(14) = 53 because the 14th prime is 43, or 101011 binary; reverse of 101011 is 110101, or 53 decimal.

Maple

a:= proc(n) local m, r; m, r:= ithprime(n), 0;
      while m>0 do r:= r*2+irem(m, 2, 'm') od; r
    end:
seq(a(n), n=1..60);  # Alois P. Heinz, Mar 08 2018

Mathematica

Table[FromDigits[Reverse[IntegerDigits[Prime[n], 2]], 2], {n, 100}] (* Alonso del Arte, Mar 05 2018 *)

Prog

(PARI) a(n)=my(v=binary(prime(n)), s); forstep(i=#v, 1, -1, s+=s+v[i]); s \\ Charles R Greathouse IV, Aug 17 2011
(Python)
from sympy import prime
def A098957(n): return int(bin(prime(n))[:1:-1], 2) # Chai Wah Wu, Feb 17 2022

Crossrefs

Cf. A000040, A030101.

Sequence in context: A137576 A161329 A111745 * A143245 A018205 A370762

Adjacent sequences: A098954 A098955 A098956 * A098958 A098959 A098960

Keyword

base,nonn

Author

Gil Broussard, Oct 21 2004

Status

approved