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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. 1
7, 19, 23, 43, 71, 101 (list; graph; refs; listen; history; text; internal format)
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

for i in range(1, 1000000, 2):

  if not isprime(i): continue

  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, A292348.

Sequence in context: A032680 A141831 A176182 * A065749 A032642 A127633

Adjacent sequences:  A292346 A292347 A292348 * A292350 A292351 A292352

KEYWORD

nonn,base,more

AUTHOR

Alex Ratushnyak, Dec 07 2017

STATUS

approved

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Last modified August 9 13:50 EDT 2020. Contains 336323 sequences. (Running on oeis4.)