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

Author

Gil Broussard, Oct 21 2004

Keywords

• base
• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000040, A030101.

Programs

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 *)

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

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