A292349 - OEIS

A292349

Pri-most primes: primes p such that the majority of bits in the binary representation of p satisfy the following: complementing this bit produces a prime number.

7, 19, 23, 43, 71, 101

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OFFSET

1,1

COMMENTS

Primes in A292348.

Conjecture: the sequence is finite.

LINKS

Table of n, a(n) for n=1..6.

MATHEMATICA

Select[Prime@ Range[10^5], Function[n, Function[d, 2 Count[Array[FromDigits[#, 2] &@ MapAt[Mod[# + 1, 2] &, d, #] &, Length@ d], _?PrimeQ] > Length@ d]@ IntegerDigits[n, 2]]] (* Michael De Vlieger, Dec 08 2017 *)

PROG

(Python)

from sympy import isprime, primerange

for i in primerange(1, 1000):

delta = 0

bit = 1

while bit <= i:

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

else: delta -= 1

bit*=2

if delta > 0: print(str(i), end=', ')

CROSSREFS