cp's OEIS Frontend

A297929 Lexicographically earliest sequence of distinct prime numbers such that for any n > 1, a(n) is at Hamming distance one from some previous term.

%I A297929 #17 Jul 25 2019 01:01:11
%S A297929 2,3,7,5,11,13,19,17,23,29,31,37,43,41,47,53,59,61,67,71,79,83,101,97,
%T A297929 103,107,109,113,131,139,137,151,149,157,163,167,179,181,199,197,193,
%U A297929 211,227,229,241,263,269,271,293,317,313,281,283,347,331,353,359
%N A297929 Lexicographically earliest sequence of distinct prime numbers such that for any n > 1, a(n) is at Hamming distance one from some previous term.
%C A297929 For any n > 1, a(n) = a(m) XOR 2^k for some m < n and k >= 0 (where XOR denotes the bitwise XOR operator).
%C A297929 This sequence was inspired by A294994.
%C A297929 Let define the binary relation R over prime numbers as follows:
%C A297929 - for any prime numbers p and q, p is R-related to q iff there exists a finite list of prime numbers, say (c(1), ..., c(k)), such that c(1) = p and c(k) = q and A000120(c(i) XOR c(i+1)) = 1 for i = 1..k-1,
%C A297929 - R is a equivalence relation,
%C A297929 - this sequence corresponds to the R-equivalence class of the prime number 2.
%C A297929 Is this sequence infinite?
%C A297929 Will every prime number appear?
%H A297929 Rémy Sigrist, <a href="/A297929/b297929.txt">Table of n, a(n) for n = 1..10000</a>
%H A297929 Rémy Sigrist, <a href="/A297929/a297929.png">Scatterplot of the first 359854 terms</a> (a(359855) is the first term > 2^23)
%H A297929 Rémy Sigrist, <a href="/A297929/a297929_1.png">Illustration of the first terms</a>
%H A297929 Rémy Sigrist, <a href="/A297929/a297929_1.gp.txt">PARI program for A297929</a>
%e A297929 See illustration of the first terms in Links section.
%t A297929 With[{nn = 56}, Nest[Function[a, Append[a, SelectFirst[Prime@ Range[3 nn/2], Function[p, And[FreeQ[a, p], AnyTrue[a, Total@ IntegerDigits[BitXor[p, #], 2] == 1 &]]]]]], {2}, nn]] (* _Michael De Vlieger_, Jan 14 2018 *)
%o A297929 (PARI) See Links section.
%Y A297929 Cf. A000120, A294994.
%K A297929 nonn,base
%O A297929 1,1
%A A297929 _Rémy Sigrist_, Jan 08 2018