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A297929 Lexicograpically earliest sequence of distinct prime numbers such that for any n > 1, a(n) is at Hamming distance one from some previous term. 1
2, 3, 7, 5, 11, 13, 19, 17, 23, 29, 31, 37, 43, 41, 47, 53, 59, 61, 67, 71, 79, 83, 101, 97, 103, 107, 109, 113, 131, 139, 137, 151, 149, 157, 163, 167, 179, 181, 199, 197, 193, 211, 227, 229, 241, 263, 269, 271, 293, 317, 313, 281, 283, 347, 331, 353, 359 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

This sequence was inspired by A294994.

Let define the binary relation R over prime numbers as follows:

- 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,

- R is a equivalence relation,

- this sequence corresponds to the R-equivalence class of the prime number 2.

Is this sequence infinite?

Will every prime number appear?

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 359854 terms (a(359855) is the first term > 2^23)

Rémy Sigrist, Illustration of the first terms

Rémy Sigrist, PARI program for A297929

EXAMPLE

See illustration of the first terms in Links section.

MATHEMATICA

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 *)

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000120, A294994.

Sequence in context: A275205 A171039 A063904 * A221858 A139317 A117928

Adjacent sequences:  A297926 A297927 A297928 * A297930 A297931 A297932

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 08 2018

STATUS

approved

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Last modified July 23 15:58 EDT 2019. Contains 325258 sequences. (Running on oeis4.)