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A292348 "Pri-most" numbers: the majority of bits in the binary representation of these numbers satisfy the following: complementing this bit produces a prime number. 2
6, 7, 15, 19, 21, 23, 27, 43, 45, 63, 71, 75, 77, 81, 99, 101, 105, 111, 135, 147, 159, 165, 175, 183, 189, 195, 225, 231, 235, 237, 243, 255, 261, 273, 285, 309, 315, 335, 345, 357, 363, 375, 381, 423, 435, 483, 495, 507, 553, 555, 573, 585, 645, 663, 669, 675 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: the sequence is infinite.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

EXAMPLE

23 is 10111 in binary, 23 XOR {1,2,4,8,16} = {22,21,19,31,7}, three times a prime was produced, namely 19,31,7, versus two composites, 22 and 21. More primes than composites, therefore 23 is a term.

MAPLE

a:= proc(n) option remember; local k; for k from 1+a(n-1) while add(

     `if`(isprime(Bits[Xor](k, 2^i)), 1, -1), i=0..ilog2(k))<1 do od; k

    end: a(0):=0:

seq(a(n), n=1..100);  # Alois P. Heinz, Dec 07 2017

MATHEMATICA

okQ[n_] := Module[{cnt, f}, cnt = Thread[f[n, 2^Range[0, Log[2, n] // Floor]]] /. f -> BitXor // PrimeQ; Count[cnt, True] > Length[cnt]/2];

Select[Range[1000], okQ] (* Jean-François Alcover, Oct 04 2019 *)

PROG

(Python)

from sympy import isprime

for i in range(1000):

  foundPrime = nonPrime = 0

  bit = 1

  while  bit <= i:

    if isprime(i^bit): foundPrime += 1

    else:              nonPrime += 1

    bit*=2

  if foundPrime > nonPrime:  print str(i)+', ',

CROSSREFS

Cf. A000040, A137985, A292349.

Sequence in context: A315842 A085512 A165767 * A319185 A196223 A106680

Adjacent sequences:  A292345 A292346 A292347 * A292349 A292350 A292351

KEYWORD

nonn,base

AUTHOR

Alex Ratushnyak, Dec 07 2017

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)