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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 08 2018
STATUS
approved