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

1,1

Comments

A053645(a(n)) is prime.

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A091931.

Cf. A118958.

Sequence in context: A152469 A115558 A067466 * A165349 A160024 A063911

Adjacent sequences: A091929 A091930 A091931 * A091933 A091934 A091935

Keyword

nonn

Author

Reinhard Zumkeller, Feb 14 2004

Status

approved