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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): delta = 0 # foundPrime - nonPrime bit = 1 while bit <= i: if isprime(i^bit): delta += 1 else: delta -= 1 bit*=2 if delta > 0: print(str(i), end=', ') 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 May 29 02:26 EDT 2023. Contains 363029 sequences. (Running on oeis4.)