A091932 Primes that remain prime when their leading digit in binary representation is replaced by 0.

7, 11, 13, 19, 23, 29, 37, 43, 61, 67, 71, 83, 101, 107, 131, 139, 151, 157, 181, 199, 211, 229, 241, 263, 269, 293, 317, 353, 359, 383, 419, 449, 467, 479, 523, 541, 571, 601, 613, 619, 643, 661, 691, 709, 739, 751, 769, 823, 829, 859, 991, 1021, 1031, 1061

Offset: 1

Author

Reinhard Zumkeller, Feb 14 2004

Keywords

• nonn

Comments

A053645(a(n)) is prime.

Primes p such that p - 2^floor(log_2(p)) is prime - T. D. Noe, Apr 08 2011

Examples

			A000040(12)=37 --> '100101' --> '[1]00101' --> '[0]00101' --> '101' --> 5, therefore 37 is a term.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A091931.

Cf. A118958.

Programs

Mathematica

Select[Prime[Range[100]], PrimeQ[# - 2^Floor[Log[2, #]]] &] (* T. D. Noe, Apr 08 2011 *)
Select[Prime[Range[200]],PrimeQ[FromDigits[Rest[ IntegerDigits[ #,2]],2]]&] (* Harvey P. Dale, Apr 08 2016 *)

Python

from sympy import isprime, primerange
def ok(p): return isprime((1 << (p.bit_length()-1)) ^ p)
def aupto(lim): return [p for p in primerange(1, lim+1) if ok(p)]
print(aupto(1061)) # Michael S. Branicky, Jul 11 2021

Formula

A118953(A049084(a(n))) = 1; subsequence of A065380. - Reinhard Zumkeller, May 07 2006